by Tiwari Academy Team
NCERT Solutions for Class 8 Maths Ganita Prakash Part 2 Chapter 1 Fractions in Disguise – Exercises Question Answers for Session 2026-27. Every percentage is a fraction in disguise: a fraction with 100 as its denominator.
NCERT Class 8 Maths Ganita Prakash Part 2 Chapter 1 Solutions
Class 8 Maths Ganita Prakash Part 2 Chapter 1, builds on this idea, showing how to move between fractions, decimals and percentages, find a percentage of a quantity, make sense of values above 100% and calculate percentage increase or decrease. It then applies these skills to profit and loss, discounts, GST, simple and compound interest with depreciation. Below, you will find step-by-step NCERT solutions to all the Figure it Out questions, with every calculation shown clearly, so you can check your homework and revise before exams.
Get here the Solutions and Answers of Figure it Out at Page 3.
Page 3 – Figure it Out
1. Express the following fractions as percentages.
(i) 3/5
(ii) 7/14
(iii) 9/20
(iv) 72/150
(v) 1/3
(vi) 5/11
Answer:
To express a fraction as a percentage, we multiply it by 100 and put the % sign.
(i) 3/5
Required percentage = (3/5 ร 100)%
= (3 ร 20)%
= 60%
โด 3/5 = 60%.
(ii) 7/14
On simplifying, we get,
7/14 = 1/2
Required percentage = (1/2 ร 100)%
= (1 ร 50)%
= 50%
โด 7/14 = 50%.
(iii) 9/20
Required percentage = (9/20 ร 100)%
= (9 ร 5)%
= 45%
โด 9/20 = 45%.
(iv) 72/150
On simplifying, we get,
72/150 = 12/25
Required percentage = (12/25 ร 100)%
= (12 ร 4)%
= 48%
โด 72/150 = 48%.
(v) 1/3
Required percentage = (1/3 ร 100)%
= (100/3)%
= 33โ
%
โด 1/3 = 33โ
%.
(vi) 5/11
Required percentage = (5/11 ร 100)%
= (500/11)%
On dividing 500 by 11, we get quotient 45 and remainder 5.
โด Required percentage = (45 + 5/11)%
= 45 5/11%
Hence, 5/11 = 45 5/11%.
2. Nandini has 25 marbles, of which 15 are white. What percentage of her marbles are white?
(i) 10%
(ii) 15%
(iii) 25%
(iv) 60%
(v) 40%
(vi) None of these
Answer:
Total number of marbles = 25
Number of white marbles = 15
Percentage of white marbles = (Number of white marbles / Total number of marbles ร 100)%
= (15/25 ร 100)%
= (15 ร 4)%
= 60%
Hence, 60% of Nandiniโs marbles are white.
The correct option is (iv) 60%.
3. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?
Answer:
Total number of students = 80
Number of students who come by walking = 15
Percentage of students who come by walking
= (Number of students who come by walking / Total number of students ร 100)%
= (15/80 ร 100)%
= (1500/80)%
= 18.75%
Hence, 18.75% of the students come to school by walking.
4. A group of friends is participating in a long-distance run. The positions of each of them after 15 minutes are shown in the following picture. Match (among the given options) what percentage of the race each of them has approximately completed.
Answer:
From the positions shown in the picture, we get the following approximate matches among the given options:
A is between one-fourth and one-half of the race. The closest given option is 38%.
B is a little beyond halfway. The closest given option is 55%.
C is about three-fourths of the way through the race. The closest given option is 72%.
D is very close to the finish. The closest given option is 93%.
Hence, the matches are:
A โ 38%
B โ 55%
C โ 72%
D โ 93%
5. Pairs of quantities are shown below. Identify and write appropriate symbols โ>โ, โ<โ, โ=โ in the blanks. Try to do it without calculations.
(i) 50% ____ 5%
(ii) 5/10 ____ 50%
(iii) 3/11 ____ 61%
(iv) 30% ____ 1/3
Answer:
(i) 50% > 5%
Fifty out of a hundred is more than five out of a hundred.
โด 50% > 5%.
(ii) 5/10 = 50%
Both 5/10 and 50% represent one-half of a whole.
โด 5/10 = 50%.
(iii) 3/11 < 61%
3/11 is less than one-half, whereas 61% is greater than one-half.
โด 3/11 < 61%.
(iv) 30% < 1/3
From Question 1, we know that 1/3 = 33โ
%, which is greater than 30%.
โด 30% < 1/3.
Get here the Solutions and Answers of Figure it Out at Page 12.
Page 12 – Figure it Out
Estimate first before making any computations to solve the following questions. Try different methods including mental computations.
1. Find the missing numbers. The first problem has been worked out.
Answer:
(i) The bar has 5 equal parts.
Each part represents 100% รท 5 = 20%.
The whole bar represents 75.
Value of 4 parts = (4/5) ร 75 = 60.
(ii) The marked length on the right is a little more than half the bar, so its value should be a little more than 45.
The bar has 10 equal parts.
Each part represents 100% รท 10 = 10%.
The whole bar represents 90.
Value of 1 part = 90 รท 10 = 9.
Value of 6 parts = 6 ร 9 = 54.
โด The missing numbers are 10% and 54.
(iii) The marked length on the right is between half and the whole bar, so its value should be between 70 and 140.
The bar has 4 equal parts.
Each part represents 100% รท 4 = 25%.
The whole bar represents 140.
Value of 1 part = 140 รท 4 = 35.
Value of 3 parts = 3 ร 35 = 105.
โด The missing numbers are 25% and 105.
2. Find the value of the following and also draw their bar models.
(i) 25% of 160
(ii) 16% of 250
(iii) 62% of 360
(iv) 140% of 40
(v) 1% of 1 hour
(vi) 7% of 10 kg
Answer:
(i) 25% of 160
25% is one-fourth, so the answer should be 40.
25% of 160 = (25/100) ร 160
= 160 รท 4
= 40.
(ii) 16% of 250
15% of 250 is 37.5, so 16% should be a little more, about 40.
10% of 250 = 25.
5% of 250 = 12.5.
1% of 250 = 2.5.
โด 16% of 250 = 25 + 12.5 + 2.5
= 40.
(iii) 62% of 360
60% of 360 is 216, so 62% should be a little more, about 220.
62% of 360 = (62/100) ร 360
= 223.2.
(iv) 140% of 40
140% is more than 100% and less than 150%, so the answer should be between 40 and 60.
100% of 40 = 40.
40% of 40 = (40/100) ร 40 = 16.
โด 140% of 40 = 40 + 16
= 56.
(v) 1% of 1 hour
1% of an hour should be less than 1 minute.
1 hour = 60 minutes = 3600 seconds.
1% of 1 hour = (1/100) ร 3600 seconds
= 36 seconds.
(vi) 7% of 10 kg
5% of 10 kg is 0.5 kg and 10% is 1 kg, so the answer should be between 0.5 kg and 1 kg.
7% of 10 kg = (7/100) ร 10 kg
= 0.7 kg
= 700 g.
The bar models are shown below.
3. Surya made 60 ml of deep orange paint, how much red paint did he use if red paint made up 3/4 of the deep orange paint?
Answer:
3/4 is more than 1/2 and less than 1, so the quantity of red paint should be between 30 ml and 60 ml.
Quantity of red paint = (3/4) ร 60 ml
= 3 ร 15 ml
= 45 ml.
โด Surya used 45 ml of red paint.
4. Pairs of quantities are shown below. Identify and write appropriate symbols โ>โ, โ<โ, โ=โ in the boxes. Visualising or estimating can help. Compute only if necessary or for verification.
(i) 50% of 510 โก 50% of 515
(ii) 37% of 148 โก 73% of 148
(iii) 29% of 43 โก 92% of 110
(iv) 30% of 40 โก 40% of 50
(v) 45% of 200 โก 10% of 490
(vi) 30% of 80 โก 24% of 64
Answer:
(i) 50% of 510 < 50% of 515.
Half of a smaller number is smaller than half of a larger number.
(ii) 37% of 148 < 73% of 148.
For the same whole, 37% is less than 73%.
(iii) 29% of 43 < 92% of 110.
29% of 43 is less than 43.
92% of 110 is more than half of 110, which is 55.
Therefore, the first quantity is smaller.
(iv) 30% of 40 < 40% of 50.
Both the percentage and the whole are smaller in the first quantity.
For verification:
30% of 40 = 12.
40% of 50 = 20.
Since 12 < 20, the required symbol is <. (v) 45% of 200 > 10% of 490.
40% of 200 is already 80, while 10% of 490 is 49.
Therefore, 45% of 200 is greater than 10% of 490.
(vi) 30% of 80 > 24% of 64.
Both the percentage and the whole are larger in the first quantity.
For verification:
30% of 80 = 24.
24% of 64 = 15.36.
Since 24 > 15.36, the required symbol is >.
5. Fill in the blanks appropriately:
(i) 30% of k is 70, 60% of k is _____, 90% of k is _____, 120% of k is ______.
(ii) 100% of m is 215, 10% of m is _____, 1% of m is ______, 6% of m is ______.
(iii) 90% of n is 270, 9% of n is ______, 18% of n is _____, 100% of n is ______.
(iv) Make 2 more such questions and challenge your peers.
Answer:
(i) 60%, 90% and 120% are 2, 3 and 4 times 30%, respectively.
60% of k = 2 ร 70 = 140.
90% of k = 3 ร 70 = 210.
120% of k = 4 ร 70 = 280.
โด The blanks are 140, 210 and 280.
(ii) 10% is one-tenth of 100%, and 1% is one-hundredth of 100%.
10% of m = 215 รท 10 = 21.5.
1% of m = 215 รท 100 = 2.15.
6% of m = 6 ร 2.15 = 12.9.
โด The blanks are 21.5, 2.15 and 12.9.
(iii) 9% is one-tenth of 90%, and 18% is twice 9%.
9% of n = 270 รท 10 = 27.
18% of n = 2 ร 27 = 54.
1% of n = 27 รท 9 = 3.
100% of n = 100 ร 3 = 300.
โด The blanks are 27, 54 and 300.
(iv) Two similar questions are:
(a) 20% of p is 50, 40% of p is _____, 60% of p is _____, 100% of p is _____.
40% of p = 2 ร 50 = 100.
60% of p = 3 ร 50 = 150.
100% of p = 5 ร 50 = 250.
โด The blanks are 100, 150 and 250.
(b) 100% of q is 360, 10% of q is _____, 5% of q is _____, 15% of q is _____.
10% of q = 360 รท 10 = 36.
5% of q = 36 รท 2 = 18.
15% of q = 36 + 18 = 54.
โด The blanks are 36, 18 and 54.
6. Fill in the blanks:
(i) 3 is ____ % of 300.
(ii) _____ is 40% of 4.
(iii) 40 is 80% of _____.
Answer:
(i) 3 is a very small part of 300, so the required percentage should be small.
Required percentage = (3/300 ร 100)%
= 1%.
โด 3 is 1% of 300.
(ii) 40% is between one-fourth and one-half, so 40% of 4 should be between 1 and 2.
40% of 4 = (40/100) ร 4
= 1.6.
โด 1.6 is 40% of 4.
(iii) Since 80% is less than 100%, the whole should be greater than 40.
80% of the number = 40.
20% of the number = 40 รท 4 = 10.
100% of the number = 5 ร 10 = 50.
โด 40 is 80% of 50.
7. Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers.
Answer:
A week has 7 days, so 1% of a week is the same as 7% of a day.
Since 10% > 7%, 10% of a day should be longer.
1 day = 24 hours.
1 week = 7 ร 24 = 168 hours.
10% of a day = (10/100) ร 24 hours
= 2.4 hours
= 144 minutes.
1% of a week = (1/100) ร 168 hours
= 1.68 hours
= 100.8 minutes.
Since 144 minutes > 100.8 minutes, 10% of a day is longer than 1% of a week.
Two similar questions are:
(a) Is 25% of an hour longer than 10% of 2 hours?
25% of an hour = (25/100) ร 60 minutes = 15 minutes.
10% of 2 hours = (10/100) ร 120 minutes = 12 minutes.
Since 15 minutes > 12 minutes, 25% of an hour is longer.
(b) Is 20% of a day longer than 5% of 4 days?
20% of a day = (20/100) ร 24 hours = 4.8 hours.
5% of 4 days = (5/100) ร 96 hours = 4.8 hours.
Both are equal. Therefore, 20% of a day is not longer than 5% of 4 days.
8. Mariamโs farm has a peculiar bull. One day she gave the bull 2 units of fodder and the bull ate 1 unit. The next day, she gave the bull 3 units of fodder and the bull ate 2 units. The day after, she gave the bull 4 units and the bull ate 3 units. This continued, and on the 99th day she gave the bull 100 units and the bull ate 99 units. Represent these quantities as percentages. This task can be distributed among the class. What do you observe?
Answer:
The bull eats half of the fodder on the first day. After that, it eats more than half and the percentage should get closer to 100%.
Percentage eaten = (Fodder eaten รท Fodder offered) ร 100%.
Day 1: Percentage eaten = (1/2 ร 100)% = 50%.
Day 2: Percentage eaten = (2/3 ร 100)% = 66โ
%.
Day 3: Percentage eaten = (3/4 ร 100)% = 75%.
Day 4: Percentage eaten = (4/5 ร 100)% = 80%.
On day n, n + 1 units are offered and n units are eaten.
โด Percentage eaten on day n = (n/(n + 1) ร 100)%.
The daily percentages are shown below. Values are rounded to two decimal places wherever needed.
Day| Eaten Day | Eaten Day | Eaten
1 | 50.00% 34 | 97.14% 67 | 98.53%
2 | 66.67% 35 | 97.22% 68 | 98.55%
3 | 75.00% 36 | 97.30% 69 | 98.57%
4 | 80.00% 37 | 97.37% 70 | 98.59%
5 | 83.33% 38 | 97.44% 71 | 98.61%
6 | 85.71% 39 | 97.50% 72 | 98.63%
7 | 87.50% 40 | 97.56% 73 | 98.65%
8 | 88.89% 41 | 97.62% 74 | 98.67%
9 | 90.00% 42 | 97.67% 75 | 98.68%
10 | 90.91% 43 | 97.73% 76 | 98.70%
11 | 91.67% 44 | 97.78% 77 | 98.72%
12 | 92.31% 45 | 97.83% 78 | 98.73%
13 | 92.86% 46 | 97.87% 79 | 98.75%
14 | 93.33% 47 | 97.92% 80 | 98.77%
15 | 93.75% 48 | 97.96% 81 | 98.78%
16 | 94.12% 49 | 98.00% 82 | 98.80%
17 | 94.44% 50 | 98.04% 83 | 98.81%
18 | 94.74% 51 | 98.08% 84 | 98.82%
19 | 95.00% 52 | 98.11% 85 | 98.84%
20 | 95.24% 53 | 98.15% 86 | 98.85%
21 | 95.45% 54 | 98.18% 87 | 98.86%
22 | 95.65% 55 | 98.21% 88 | 98.88%
23 | 95.83% 56 | 98.25% 89 | 98.89%
24 | 96.00% 57 | 98.28% 90 | 98.90%
25 | 96.15% 58 | 98.31% 91 | 98.91%
26 | 96.30% 59 | 98.33% 92 | 98.92%
27 | 96.43% 60 | 98.36% 93 | 98.94%
28 | 96.55% 61 | 98.39% 94 | 98.95%
29 | 96.67% 62 | 98.41% 95 | 98.96%
30 | 96.77% 63 | 98.44% 96 | 98.97%
31 | 96.88% 64 | 98.46% 97 | 98.98%
32 | 96.97% 65 | 98.48% 98 | 98.99%
33 | 97.06% 66 | 98.51% 99 | 99%
On the 99th day:
Percentage eaten = (99/100 ร 100)% = 99%.
We observe that:
โข The percentage of fodder eaten increases each day.
โข It gets closer to 100%, but stays below 100%.
โข The bull leaves 1 unit every day.
โข This 1 unit becomes a smaller percentage of the increasing amount offered.
9. Workers in a coffee plantation take 18 days to pick coffee berries in 20% of the plantation. How many days will they take to complete the picking work for the entire plantation, assuming the rate of work stays the same? Why is this assumption necessary?
Answer:
20% is one-fifth of the plantation, so the whole plantation should take 5 times as long, about 90 days.
Time taken for 20% of the plantation = 18 days.
Time taken for 100% of the plantation = (100 รท 20) ร 18 days
= 5 ร 18 days
= 90 days.
โด They will take 90 days in all to complete the work.
After the first 18 days, they will need 90 โ 18 = 72 more days.
The same rate is necessary because we are assuming that equal portions of the plantation take equal amounts of time. If the workers pick faster or slower, the total time will change.
10. The badminton coach has planned the training sessions such that the ratio of warm up : play : cool down is 10% : 80% : 10%. If he wants to conduct a training of 90 minutes. How long should each activity be done?
Answer:
Most of the time should be spent playing. Warm up and cool down should take equal amounts of time, each close to 10 minutes.
Warm up time = (10/100) ร 90 minutes
= 9 minutes.
Play time = (80/100) ร 90 minutes
= 72 minutes.
Cool down time = (10/100) ร 90 minutes
= 9 minutes.
Check: 9 + 72 + 9 = 90 minutes.
โด Warm up: 9 minutes; play: 72 minutes; cool down: 9 minutes.
11. An estimated 90% of the worldโs population lives in the Northern Hemisphere. Find the (approximate) number of people living in the Northern Hemisphere based on this yearโs worldwide population.
Answer:
Taking the approximate world population as 8.2 billion (2025 estimate), 90% should be a little less than 8.2 billion, between 7 billion and 8 billion.
Population living in the Northern Hemisphere
= (90/100) ร 8.2 billion
= 7.38 billion
= 738 crore.
โด Using the 2025 estimate, approximately 7.38 billion people or 738 crore people, live in the Northern Hemisphere.
For any other year, the approximate number is 0.9 ร that yearโs world population.
12. A recipe for the dish, halwa, for 4 people has the following ingredients in the given proportions – Rava: 40%, Sugar: 40%, and Ghee: 20%.
(i) If you want to make halwa for 8 people, what is the proportion of each of the above ingredients?
(ii) If the total weight of the ingredients is 2 kg, how much rava, sugar and ghee are present?
Answer:
(i) For twice as many people, we need twice the quantity of every ingredient. Since all the quantities are doubled, their proportions remain the same.
โด Rava = 40%, sugar = 40% and ghee = 20%.
Their ratio is 40 : 40 : 20 = 2 : 2 : 1.
(ii) Rava and sugar should have equal weights, each less than 1 kg. Ghee should weigh half as much as either one.
Weight of rava = (40/100) ร 2 kg
= 0.8 kg
= 800 g.
Weight of sugar = (40/100) ร 2 kg
= 0.8 kg
= 800 g.
Weight of ghee = (20/100) ร 2 kg
= 0.4 kg
= 400 g.
Check: 800 g + 800 g + 400 g = 2000 g = 2 kg.
โด Rava = 800 g, sugar = 800 g and ghee = 400 g.
Get here the Solutions and Answers of Figure it Out at Page 19.
Page 19 – Figure it Out
1. If a shopkeeper buys a geometry box for โน75 and sells it for โน110, what is his profit margin with respect to the cost?
Answer:
Cost price = โน75
Selling price = โน110
Profit = Selling price โ Cost price
= โน110 โ โน75
= โน35
Profit percentage = (Profit รท Cost price) ร 100%
= (35/75 ร 100)%
= (140/3)%
= 46โ
%
โด His profit margin with respect to the cost is 46โ
%.
2. I am a carpenter and I make chairs. The cost of materials for a chair is โน475 and I want to have a profit margin of 50%. At what price should I sell a chair?
Answer:
Cost price of a chair = โน475
Required profit = 50% of โน475
= โน(50/100 ร 475)
= โน237.50
Selling price = Cost price + Profit
= โน475 + โน237.50
= โน712.50
โด I should sell a chair for โน712.50.
3. The total sales of a company (also called revenue) was โน2.5 crore last year. They had a healthy profit margin of 25%. What was the total expenditure (costs) of the company last year?
Answer:
Total sales = โน2.5 crore
Here, the profit is 25% of the total sales.
Profit = 25% of โน2.5 crore
= โน(25/100 ร 2.5) crore
= โน0.625 crore
Total expenditure = Total sales โ Profit
= โน2.5 crore โ โน0.625 crore
= โน1.875 crore
โด The total expenditure was โน1.875 crore, or โน1,87,50,000.
4. A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is โน300, how much will Anwar have to pay to buy this shirt?
Answer:
Original price = โน300
Discount = 25% of โน300
= โน(25/100 ร 300)
= โน75
Amount to be paid = Original price โ Discount
= โน300 โ โน75
= โน225
โด Anwar will have to pay โน225.
5. The petrol price in 2015 was โน60 and โน100 in 2025. What is the percentage increase in the price of petrol?
(i) 50%
(ii) 40%
(iii) 60%
(iv) 66.66%
(v) 140%
(vi) 160.66%
Answer:
Increase in price = โน100 โ โน60 = โน40
Percentage increase = (Increase รท Original price) ร 100%
= (40/60 ร 100)%
= (200/3)%
= 66โ
%
โด The increase is 66โ
% = 66.666โฆ%.
The closest option is (iv), 66.66%.
6. Samson bought a car for โน4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car?
Answer:
After a discount of 15%, Samson paid 100% โ 15% = 85% of the original price.
85% of the original price = โน4,40,000
1% of the original price = โน(4,40,000 รท 85)
100% of the original price = โน(4,40,000 ร 100 รท 85)
= โน(88,00,000/17)
โ โน5,17,647.06
โด The original price of the car was approximately โน5,17,647.06.
7. 1600 people voted in an election and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for the election?
Answer:
Percentage of votes received by the winner = (500/1600 ร 100)%
= 31.25%
The winner got the most votes, so no other candidate could have received more than 500 votes.
If there were only 3 candidates, their total votes could not be more than 3 ร 500 = 1500.
But 1600 votes were cast. So, at least 4 candidates must have stood for the election.
For example, the votes could be 500, 400, 400 and 300.
Their sum is 1600 and the candidate with 500 votes wins.
โด The winner got 31.25% of the votes and the minimum number of candidates is 4.
8. The price of 1 kg of rice was โน38 in 2024. It is โน42 in 2025. What is the rate of inflation? (Inflation is the percentage increase in prices.)
Answer:
Increase in price = โน42 โ โน38 = โน4
Rate of inflation = (Increase รท Original price) ร 100%
= (4/38 ร 100)%
= (200/19)%
โ 10.53%
โด The rate of inflation is approximately 10.53%.
9. A number increased by 20% becomes 90. What is the number?
Answer:
After an increase of 20%, the new number is 120% of the original number.
120% of the original number = 90
Original number = 90 ร 100/120
= 75
โด The number is 75.
10. A milkman sold two buffaloes for โน80,000 each. On one of them, he made a profit of 5% and on the other a loss of 10%. Find his overall profit or loss.
Answer:
For the first buffalo, the selling price is 105% of its cost price.
Cost price of the first buffalo = โน(80,000 ร 100/105)
= โน(16,00,000/21)
For the second buffalo, the selling price is 90% of its cost price.
Cost price of the second buffalo = โน(80,000 ร 100/90)
= โน(8,00,000/9)
Total cost price = โน(16,00,000/21 + 8,00,000/9)
= โน(48,00,000/63 + 56,00,000/63)
= โน(1,04,00,000/63)
โ โน1,65,079.37
Total selling price = โน80,000 + โน80,000
= โน1,60,000
Since the total cost price is greater than the total selling price, there is a loss.
Loss = โน(1,04,00,000/63 โ 1,60,000)
= โน(3,20,000/63)
โ โน5,079.37
Loss percentage = (Loss รท Total cost price) ร 100%
= [(3,20,000/63) รท (1,04,00,000/63) ร 100]%
= (40/13)%
โ 3.08%
โด His overall loss is approximately โน5,079.37, or 3.08%.
11. The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants last decade is p, the population now is
(i) p ร 0.5
(ii) p ร 0.05
(iii) p ร 1.5
(iv) p ร 1.05
(v) p + 1.50
Answer:
Increase in population = 5% of p = 0.05p
Present population = p + 0.05p = 1.05p
โด The correct option is (iv) p ร 1.05.
12. Which of the following statement(s) mean the same as – โThe demand for cameras has fallen by 85% in the last decadeโ?
(i) The demand now is 85% of the demand a decade ago.
(ii) The demand a decade ago was 85% of the demand now.
(iii) The demand now is 15% of the demand a decade ago.
(iv) The demand a decade ago was 15% of the demand now.
(v) The demand a decade ago was 185% of the demand now.
(vi) The demand now is 185% of the demand a decade ago.
Answer:
Let the demand a decade ago be 100 units.
A fall of 85% means a decrease of 85 units.
Demand now = 100 โ 85 = 15 units.
โด The demand now is 15% of the demand a decade ago.
The correct option is (iii).
Get here the Solutions and Answers of Figure it Out at Page 22.
Page 22 – Figure it Out
1. Bank of Yahapur offers an interest of 10% p.a. Compare how much one gets if they deposit โน20,000 for a period of 2 years with compounding and without compounding annually.
Answer:
Without compounding:
Interest for 1 year = 10% of โน20,000
= โน(10/100 ร 20,000)
= โน2,000
Interest for 2 years = โน2,000 ร 2 = โน4,000
Total amount received = โน20,000 + โน4,000 = โน24,000
With annual compounding:
Interest for the first year = 10% of โน20,000 = โน2,000
Amount after the first year = โน20,000 + โน2,000 = โน22,000
Interest for the second year = 10% of โน22,000 = โน2,200
Amount after the second year = โน22,000 + โน2,200 = โน24,200
Difference = โน24,200 โ โน24,000 = โน200
โด One gets โน24,000 without compounding and โน24,200 with annual compounding. Compounding gives โน200 more.
2. Bank of Wahapur offers an interest of 5% p.a. Compare how much one gets if one deposits โน20,000 for a period of 4 years with compounding and without compounding annually.
Answer:
Without compounding:
Interest for 1 year = 5% of โน20,000 = โน1,000
Interest for 4 years = โน1,000 ร 4 = โน4,000
Total amount received = โน20,000 + โน4,000 = โน24,000
With annual compounding:
Year 1:
Interest = 5% of โน20,000 = โน1,000
Amount = โน20,000 + โน1,000 = โน21,000
Year 2:
Interest = 5% of โน21,000 = โน1,050
Amount = โน21,000 + โน1,050 = โน22,050
Year 3:
Interest = 5% of โน22,050 = โน1,102.50
Amount = โน22,050 + โน1,102.50 = โน23,152.50
Year 4:
Interest = 5% of โน23,152.50 = โน1,157.625
Amount = โน23,152.50 + โน1,157.625 = โน24,310.125
Rounding the final amount to the nearest paise, we get โน24,310.13.
Extra amount from compounding = โน24,310.125 โ โน24,000
= โน310.125
โ โน310.13
โด One gets โน24,000 without compounding and approximately โน24,310.13 with annual compounding. Compounding gives approximately โน310.13 more.
3. Do you observe anything interesting in the solutions of the two questions above? Share and discuss.
Answer:
Without compounding, both deposits give the same total interest of โน4,000 and the same total amount of โน24,000.
This is because 10% ร 2 = 20% and 5% ร 4 = 20%. In both cases, the total interest is 20% of โน20,000.
With annual compounding:
Amount from Bank of Yahapur after 2 years = โน24,200
Amount from Bank of Wahapur after 4 years = โน24,310.125
Difference = โน24,310.125 โ โน24,200
= โน110.125
โ โน110.13
So, Bank of Wahapur gives approximately โน110.13 more over its 4-year period, even though its annual interest rate is lower.
With compounding, each year’s interest is added to the deposit and also earns interest in the following years. In these two cases, the longer period of 4 years gives a greater final amount.
Get here the Solutions and Answers of Figure it Out at Page 24.
Page 24 – Figure it Out
4. Jasmine invests amount โpโ for 4 years at an interest of 6% p.a. Which of the following expression(s) describe the total amount she will get after 4 years when compounding is not done?
(i) p ร 6 ร 4
(ii) p ร 0.6 ร 4
(iii) p ร (0.6/100) ร 4
(iv) p ร (0.06/100) ร 4
(v) p ร 1.6 ร 4
(vi) p ร 1.06 ร 4
(vii) p + (p ร 0.06 ร 4)
Answer:
Interest for 1 year = 6% of p
= p ร 6/100
= p ร 0.06
Without compounding, the interest is the same each year.
Interest for 4 years = p ร 0.06 ร 4
Total amount = Principal + Interest
= p + (p ร 0.06 ร 4)
= 1.24p
โด The correct option is (vii).
5. The post office offers an interest of 7% p.a. How much interest would one get if one invests โน50,000 for 3 years without compounding? How much more would one get if it was compounded?
Answer:
Without compounding:
Interest for 1 year = 7% of โน50,000 = โน3,500
Interest for 3 years = โน3,500 ร 3 = โน10,500
With annual compounding:
Year 1:
Interest = 7% of โน50,000 = โน3,500
Amount = โน50,000 + โน3,500 = โน53,500
Year 2:
Interest = 7% of โน53,500 = โน3,745
Amount = โน53,500 + โน3,745 = โน57,245
Year 3:
Interest = 7% of โน57,245 = โน4,007.15
Amount = โน57,245 + โน4,007.15 = โน61,252.15
Compound interest for 3 years = โน61,252.15 โ โน50,000
= โน11,252.15
Extra interest = โน11,252.15 โ โน10,500
= โน752.15
โด The interest without compounding is โน10,500. Annual compounding gives โน752.15 more.
6. Giridhar borrows a loan of โน12,500 at 12% per annum for 3 years without compounding and Raghava borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Answer:
Giridhar’s loan:
Interest for 1 year = 12% of โน12,500
= โน(12/100 ร 12,500)
= โน1,500
Interest for 3 years = โน1,500 ร 3 = โน4,500
Raghava’s loan:
Amount after the first year = โน12,500 ร 1.10 = โน13,750
Amount after the second year = โน13,750 ร 1.10 = โน15,125
Amount after the third year = โน15,125 ร 1.10 = โน16,637.50
Interest for 3 years = โน16,637.50 โ โน12,500
= โน4,137.50
Difference in interest = โน4,500 โ โน4,137.50
= โน362.50
โด Giridhar pays โน362.50 more interest than Raghava.
7. Consider an amount โน1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when compounding is not done? Is compounding an example of exponential growth and not-compounding an example of linear growth?
Answer:
Double of โน1000 = โน2000
So, the required increase is โน2000 โ โน1000 = โน1000.
Without compounding:
Interest each year = 10% of โน1000 = โน100
Time required = โน1000 รท โน100 per year = 10 years
With annual compounding:
Each year, the amount becomes 110% of the previous year’s amount. So, we multiply by 1.1 each year.
After 1 year: โน1000 ร 1.1 = โน1100
After 2 years: โน1100 ร 1.1 = โน1210
After 3 years: โน1210 ร 1.1 = โน1331
After 4 years: โน1331 ร 1.1 = โน1464.1
After 5 years: โน1464.1 ร 1.1 = โน1610.51
After 6 years: โน1610.51 ร 1.1 = โน1771.561
After 7 years: โน1771.561 ร 1.1 = โน1948.7171
After 8 years: โน1948.7171 ร 1.1 = โน2143.58881
The amount is less than โน2000 after 7 years and more than โน2000 after 8 years.
โด With annual compounding, it first reaches or exceeds double at the end of 8 years. Without compounding, it doubles in 10 years.
Yes, compounding is an example of exponential growth because the amount is multiplied by the same factor, 1.1, each year. Without compounding, it is linear growth because the same amount, โน100, is added each year.
8. The population of a city is rising by about 3% every year. If the current population is 1.5 crore, what is the expected population after 3 years?
Answer:
Current population = 1.5 crore = 1,50,00,000
Each year, the population becomes 103% of the previous year’s population.
Multiplying factor = 103/100 = 1.03
Population after 1 year = 1,50,00,000 ร 1.03 = 1,54,50,000
Population after 2 years = 1,54,50,000 ร 1.03 = 1,59,13,500
Population after 3 years = 1,59,13,500 ร 1.03 = 1,63,90,905
โด The expected population after 3 years is about 1,63,90,905, or 1.6390905 crore.
9. In a laboratory, the number of bacteria in a certain experiment increases at the rate of 2.5% per hour. Find the number of bacteria at the end of 2 hours if the initial count is 5,06,000.
Answer:
Initial number of bacteria = 5,06,000
Each hour, the number becomes 102.5% of the previous count.
Multiplying factor = 102.5/100 = 1.025
Number after 1 hour = 5,06,000 ร 1.025
= 5,18,650
Number after 2 hours = 5,18,650 ร 1.025
= 5,31,616.25
As per calculation, it is 5,31,616.25. Since bacteria are counted in whole numbers, the expected count is approximately 5,31,616 bacteria.
Get here the Solutions and Answers of Figure it Out at Page 28.
Page 28 – Figure it Out
1. The population of Bengaluru in 2025 is about 250% of its population in 2000. If the population in 2000 was 50 lakhs, what is the population in 2025?
Answer:
Population in 2025 = 250% of 50 lakhs
= (250/100) ร 50 lakhs
= 125 lakhs
โด The population in 2025 is about 125 lakhs or 1 crore 25 lakhs.
2. The population of the world in 2025 is about 8.2 billion. The populations of some countries in 2025 are given. Match them with their approximate percentage share of the worldwide population.
[Hint: Writing these numbers in the standard form and estimating can help].
Answer:
World population = 8.2 billion = 8,200 million
India’s population = 1.46 billion = 1,460 million
Percentage share = (Country’s population รท World population) ร 100%
Germany’s share = (83/8,200 ร 100)%
โ 1.01%
โ 1%
India’s share = (1,460/8,200 ร 100)%
โ 17.80%
โ 18%
Bangladesh’s share = (175/8,200 ร 100)%
โ 2.13%
โ 2%
USA’s share = (347/8,200 ร 100)%
โ 4.23%
โ 4%
โด The matches are:
Germany โ 1%
India โ 18%
Bangladesh โ 2%
USA โ 4%
The option 4% is missing from the choices, while 2% appears twice.
3. The price of a mobile phone is โน8,250. A GST of 18% is added to the price. Which of the following gives the final price of the phone including the GST?
(i) 8250 + 18
(ii) 8250 + 1800
(iii) 8250 + 18/100
(iv) 8250 ร 18
(v) 8250 ร 1.18
(vi) 8250 + 8250 ร 0.18
(vii) 1.8 ร 8250
Answer:
GST = 18% of โน8,250
= โน(8,250 ร 18/100)
= โน1,485
Final price = โน8,250 + โน1,485
= โน9,735
We can also write the final price as:
8250 + 8250 ร 0.18
= 8250 ร (1 + 0.18)
= 8250 ร 1.18
โด Options (v) and (vi) are correct. The final price is โน9,735.
4. The monthly percentage change in population (compared to the previous month) of mice in a lab is given: Month 1 change was +5%, Month 2 change was โ2%, and Month 3 change was โ3%. Which of the following statement(s) are true? The initial population is p.
(i) The population after three months was p ร 0.05 ร 0.02 ร 0.03.
(ii) The population after three months was p ร 1.05 ร 0.98 ร 0.97.
(iii) The population after three months was p + 0.05 โ 0.02 โ 0.03.
(iv) The population after three months was p.
(v) The population after three months was more than p.
(vi) The population after three months was less than p.
Answer:
Population after Month 1 = p ร 105/100 = p ร 1.05
Population after Month 2 = p ร 1.05 ร 98/100
= p ร 1.05 ร 0.98
Population after Month 3 = p ร 1.05 ร 0.98 ร 97/100
= p ร 1.05 ร 0.98 ร 0.97
= 0.99813p
Since 0.99813 is less than 1, the final population is less than p.
โด Statements (ii) and (vi) are true.
5. A shopkeeper initially set the price of a product with a 35% profit margin. Due to poor sales, he decided to offer a 30% discount on the selling price. Will he make a profit or a loss? Give reasons for your answer.
Answer:
Let the cost price be โน100.
Price before discount = โน100 + 35% of โน100
= โน100 + โน35
= โน135
Discount = 30% of โน135
= โน(30/100 ร 135)
= โน40.50
Final selling price = โน135 โ โน40.50
= โน94.50
Since the selling price is less than the cost price, there is a loss.
Loss = โน100 โ โน94.50 = โน5.50
Loss percentage = (5.50/100 ร 100)% = 5.5%
โด The shopkeeper makes a loss of 5.5%.
6. What percentage of area is occupied by the region marked โEโ in the figure?
Answer:
The whole figure is a square. Its lower-left quarter is divided into two equal triangles, D and E.
Fraction of the whole area occupied by E = 1/2 ร 1/4
= 1/8
Required percentage = (1/8 ร 100)%
= 12.5%
โด Region E occupies 12.5% of the total area.
7. What is 5% of 40? What is 40% of 5?
What is 25% of 12? What is 12% of 25?
What is 15% of 60? What is 60% of 15?
What do you notice?
Can you make a general statement and justify it using algebra, comparing x% of y and y% of x?
Answer:
5% of 40 = 5/100 ร 40 = 2
40% of 5 = 40/100 ร 5 = 2
25% of 12 = 25/100 ร 12 = 3
12% of 25 = 12/100 ร 25 = 3
15% of 60 = 15/100 ร 60 = 9
60% of 15 = 60/100 ร 15 = 9
We notice that the answers in each pair are equal.
In general, x% of y = y% of x.
This is because:
x% of y = x/100 ร y = xy/100
y% of x = y/100 ร x = yx/100 = xy/100
โด x% of y and y% of x are always equal.
8. A school is organising an excursion for its students. 40% of them are Grade 8 students and the rest are Grade 9 students. Among these Grade 8 students, 60% are girls.
[Hint: Drawing a rough diagram can help].
(i) What percentage of the students going to the excursion are Grade 8 girls?
(ii) If the total number of students going to the excursion is 160, how many of them are Grade 8 girls?
Answer:
(i) Grade 8 girls are 60% of the 40% who are Grade 8 students.
Percentage of all students who are Grade 8 girls = (60/100 ร 40)%
= 24%
โด 24% of the students going to the excursion are Grade 8 girls.
(ii) Number of Grade 8 students = 40% of 160
= 40/100 ร 160
= 64
Number of Grade 8 girls = 60% of 64
= 60/100 ร 64
= 38.4
A number of students must be a whole number. Since we get 38.4, the figures in this question do not give a possible exact number of Grade 8 girls.
9. A shopkeeper sells pencils at a price such that the selling price of 3 pencils is equal to the cost of 5 pencils. Does he make a profit or a loss? What is his profit or loss percentage?
Answer:
Let the cost price of one pencil be โน1.
Cost price of 3 pencils = โน3
Cost price of 5 pencils = โน5
Selling price of 3 pencils = Cost price of 5 pencils = โน5
Since the selling price is greater than the cost price, there is a profit.
Profit on 3 pencils = โน5 โ โน3 = โน2
Profit percentage = (Profit รท Cost price) ร 100%
= (2/3 ร 100)%
= (200/3)%
= 66โ
%
โด The shopkeeper makes a profit of 66โ
%.
10. The bus fares were increased by 3% last year and by 4% this year. What is the overall percentage price increase in the last 2 years?
Answer:
Let the original fare be โน100.
Fare after last year’s increase = โน100 ร 103/100
= โน103
Fare after this year’s increase = โน103 ร 104/100
= โน107.12
Total increase = โน107.12 โ โน100
= โน7.12
Overall percentage increase = (7.12/100 ร 100)%
= 7.12%
โด The overall increase in bus fares is 7.12%.
11. If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by?
Answer:
Let the original length be l and the original breadth be b.
Original area = l ร b
New length = l ร 110/100 = 11l/10
Since the area is unchanged,
New breadth = Original area รท New length
= (l ร b) รท (11l/10)
= 10b/11
Decrease in breadth = b โ 10b/11
= b/11
Percentage decrease = [(b/11) รท b ร 100]%
= (100/11)%
= 9 1/11%
โด The breadth decreases by exactly 9 1/11%.
12. The percentage of ingredients in a 65 g chips packet is shown in the picture. Find out the weight each ingredient makes up in this packet.
Answer:
Weight of potato = 70% of 65 g
= 70/100 ร 65 g
= 45.5 g
Weight of vegetable oil = 24% of 65 g
= 24/100 ร 65 g
= 15.6 g
Weight of salt = 3% of 65 g
= 3/100 ร 65 g
= 1.95 g
Weight of spices = 3% of 65 g
= 3/100 ร 65 g
= 1.95 g
โด The packet contains approximately 45.5 g of potato, 15.6 g of vegetable oil, 1.95 g of salt and 1.95 g of spices.
13. Three shops sell the same items at the same price. The shops offer deals as follows:
Shop A: โBuy 1 and get 1 freeโ
Shop B: โBuy 2 and get 1 freeโ
Shop C: โBuy 3 and get 1 freeโ
Answer the following:
(i) If the price of one item is โน100, what is the effective price per item in each shop? Arrange the shops from cheapest to costliest.
(ii) For each shop, calculate the percentage discount on the items. [Hint: Compare the free items to the total items you receive.]
(iii) Suppose you need 4 items. Which shop would you choose? Why?
Answer:
(i) Shop A:
We pay โน100 and receive 2 items.
Effective price per item = โน100 รท 2 = โน50
Shop B:
We pay โน200 and receive 3 items.
Effective price per item = โน200 รท 3 = โน66โ
(approximately โน66.67)
Shop C:
We pay โน300 and receive 4 items.
Effective price per item = โน300 รท 4 = โน75
โด From cheapest to costliest: Shop A, Shop B, Shop C.
(ii) Discount percentage = (Number of free items รท Total number of items received) ร 100%
Shop A: (1/2 ร 100)% = 50%
Shop B: (1/3 ร 100)% = 33โ
%
Shop C: (1/4 ร 100)% = 25%
โด The discounts are 50% at Shop A, 33โ
% at Shop B and 25% at Shop C.
(iii) At Shop A, we can use the offer twice: pay for 2 items and get 2 free.
Cost of 4 items = โน200
At Shop B, we pay โน200 for 3 items under the offer and โน100 for one more item.
Cost of 4 items = โน300
At Shop C, we pay for 3 items and get 1 free.
Cost of 4 items = โน300
โด I would choose Shop A because 4 items cost only โน200, which is โน100 less than at either of the other shops.
14. In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 98%?
Answer:
Number of left-handed people = 99% of 100 = 99
Number of people who are not left-handed = 100 โ 99 = 1
Only left-handed people leave, so this 1 person remains.
When 98% are left-handed, the remaining 2% are not left-handed.
So, 2% of the remaining people = 1
Total number of people remaining = 1 ร 100/2 = 50
Number of left-handed people who leave = 100 โ 50 = 50
โด 50 left-handed people have to leave the room.
15. Look at the following graph.
Based on the graph, which of the following statement(s) are valid?
(i) People in their twenties are the most computer-literate among all age groups.
(ii) Women lag behind in the ability to use computers across age groups.
(iii) There are more people in their twenties than teenagers.
(iv) More than a quarter of people in their thirties can use computers.
(v) Less than 1 in 10 aged 60 and above can use computers.
(vi) Half of the people in their twenties can use computers.
Answer:
(i) Valid. The percentages for both women and men are highest in their twenties: 26% and 37%, respectively.
(ii) Valid. In every age group, the bar for women is shorter than the bar for men.
(iii) Not valid. The graph shows percentages of people who can use computers. It does not show the total number of people in each age group.
(iv) Not valid. A quarter is 25%. Among people in their thirties, 14% of women and 25% of men can use computers. So the overall percentage cannot be more than 25%.
(v) Valid. One in ten means 10%. Among seniors, 2% of women and 4% of men can use computers. Both are less than 10%.
(vi) Not valid. Half means 50%. Among people in their twenties, 26% of women and 37% of men can use computers. So the overall percentage is less than 50%. We cannot add these two percentages because they are percentages of different groups.
โด Statements (i), (ii) and (v) are valid.
Final Tips to Master Percentages in Class 8
Percentages are everywhere, from sale tags and GST bills to bank interest and exam scores, so this chapter will serve you well beyond your Maths test. Try each question on your own first, estimate the answer before calculating, and then use these Fractions in Disguise Class 8 solutions to check your method, not just the final number. Give extra time to the Tricky Percentages section, especially successive discounts and a 50% profit margin followed by a 50% discount, because the obvious answer turns out to be wrong. When you are ready, move on to Chapter 2, The Baudhayana-Pythagoras Theorem, or browse the other chapters in our NCERT Solutions for Class 8 Maths.
