Percentages

: How Close Can You Get?

Make a pair. Each of you choose a number. Suppose, the numbers chosen are $a$ and $b$. Share your numbers with each other. Both of you should estimate the percentage equivalent to the fraction $\frac{a}{b}$ (where $a < b$) and announce your answers by a fixed time, say, 5 seconds. The one whose estimate is the closest wins this round. Play this for 10 rounds.

Peaceful Knights

Place 8 knights on the chess board so that no knight attacks another. A knight moves in an 'L-shape'. It can move either (a) two steps vertically and one step horizontally, or (b) two steps horizontally and one step vertically. Possible moves of a knight are shown below.

Express the following fractions as percentages.

(i) $\frac{3}{5}$

(ii) $\frac{7}{14}$

(iii) $\frac{9}{20}$

(iv) $\frac{72}{150}$

(v) $\frac{1}{3}$

(vi) $\frac{5}{11}$

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

In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

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.

Pairs of quantities are shown below. Identify and write appropriate symbols '>', '<', '=' in the blanks. Try to do it without calculations.

(i) $50\% \text{ \_\_\_\_\_\_\_ } 5\%$

(ii) $\frac{5}{10} \text{ \_\_\_\_\_\_\_ } 50\%$

(iii) $\frac{3}{11} \text{ \_\_\_\_\_\_\_ } 61\%$

(iv) $30\% \text{ \_\_\_\_\_\_\_ } \frac{1}{3}$

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.

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

Surya made 60 ml of deep orange paint, how much red paint did he use if red paint made up $\frac{3}{4}$ of the deep orange paint?

Pairs of quantities are shown below. Identify and write appropriate symbols '>', '<', '=' in the boxes. Visualising or estimating can help. Compute only if necessary or for verification.

Fill in the blanks appropriately:

Fill in the blanks:

Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers.

Mariam's 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?

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?

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?

An estimated 90% of the world’s population lives in the Northern Hemisphere. Find the (approximate) number of people living in the Northern Hemisphere based on this year’s worldwide population.

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?

If a shopkeeper buys a geometry box for ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?

I am a carpenter and I make chairs. The cost of materials for a chair is ₹475 and I want to have a profit margin of 50%. At what price should I sell a chair?

The total sales of a company (also called revenue) was ₹2.5 crore last year. They had a healthy profit margin of 25%. What was the total expenditure (costs) of the company last year?

A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is ₹300, how much will Anwar have to pay to buy this shirt?

The petrol price in 2015 was ₹60 and ₹100 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%

Samson bought a car for ₹4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car?

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?

The price of 1 kg of rice was ₹38 in 2024. It is ₹42 in 2025. What is the rate of inflation? (Inflation is the percentage increase in prices.)

A number increased by 20% becomes 90. What is the number?

A milkman sold two buffaloes for ₹80,000 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.

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) $p \times 0.5$

(ii) $p \times 0.05$

(iii) $p \times 1.5$

(iv) $p \times 1.05$

(v) $p + 1.50$

Which of the following statement(s) mean the same as — "The demand for cameras has fallen by 85% in the last decade"?

(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.

Bank of Yahapur offers an interest of 10% p.a. Compare how much one gets if they deposit ₹20,000 for a period of 2 years with compounding and without compounding annually.

Bank of Wahapur offers an interest of 5% p.a. Compare how much one gets if one deposits ₹20,000 for a period of 4 years with compounding and without compounding annually.

Do you observe anything interesting in the solutions of the two questions above? Share and discuss.

Jasmine invests amount 'p' 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) $p \times 6 \times 4$

(ii) $p \times 0.6 \times 4$

(iii) $p \times \frac{0.6}{100} \times 4$

(iv) $p \times \frac{0.06}{100} \times 4$

(v) $p \times 1.6 \times 4$

(vi) $p \times 1.06 \times 4$

(vii) $p + (p \times 0.06 \times 4)$

The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹50,000 for 3 years without compounding? How much more would one get if it was compounded?

Giridhar borrows a loan of ₹12,500 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?

Consider an amount ₹1000. 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?

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?

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.

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?

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].

The price of a mobile phone is ₹8,250. 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) $8250 + \frac{18}{100}$

(iv) $8250 \times 18$

(v) $8250 \times 1.18$

(vi) $8250 + 8250 \times 0.18$

(vii) $1.8 \times 8250$

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 –2%, and Month 3 change was –3%. Which of the following statement(s) are true? The initial population is $p$.

(i) The population after three months was $p \times 0.05 \times 0.02 \times 0.03$.

(ii) The population after three months was $p \times 1.05 \times 0.98 \times 0.97$.

(iii) The population after three months was $p + 0.05 - 0.02 - 0.03$.

(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 $p$.

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.

What percentage of area is occupied by the region marked ‘E’ in the figure?

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?

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?

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?

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?

If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by?

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.

Three shops sell the same items at the same price. The shops offer deals as follows: Shop A: "Buy 1 and get 1 free" Shop B: "Buy 2 and get 1 free" Shop C: "Buy 3 and get 1 free"

Answer the following:

(i) If the price of one item is ₹100, 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?

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%?

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.

Can you tell what percentage of the colour was made using yellow?

Try completing Method 3 by filling the boxes.

Try to calculate (without using pen and paper) the indicated percentages of the values shown in the table below. Write your answers in the table.

How did you find these values? Discuss the methods with the class. Do you find anything interesting in the table?

Using this understanding, mentally calculate how much 40% of the values in the table above would be.

What relationship do you observe among 20%, 5%, and 25% of a value?

Using this observation, mentally calculate how much 15% of the values in the table would be.

Suppose you have to mentally calculate the following percentages of some value: 75%, 90%, 70%, 55%. How would you do it? Discuss.

Similarly, to find 10% of a quantity, what decimal value should be multiplied?

Complete the following table:

Context: Kishanlal's daily sales target is ₹5000.

Q. On Days 5 and 6 his sales were ₹7800 and ₹9550 respectively. Calculate the percentage of the target achieved on these days.

Context: Kishanlal's daily sales target is ₹5000.

Q. On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days.

Complete the table below. Mark the approximate locations in the following diagram.

Complete this table by calculating the percentages to answer the questions:

• Which product has a larger share of badam?
• Which product uses a smaller proportion of food chemicals?

Check if the percentages of each product add up to 100.

Find the profit percentage of the wholesaler and the manufacturer.

Shambhavi owns a stationery shop. She procures 200 page notebooks at ₹36 per book. She sells them with a profit margin of 20%. Find the selling price.

She sells crayon boxes at ₹50 per box with a profit margin of 25%. How much did Shambhavi buy them from the wholesaler?

Context: Raghu purchased rice at ₹35 per kg and sold 10 kg of it for ₹300.

Q. Could we have just calculated the loss percentage per kg instead? Would it be the same?

Context: Shyamala had procured decorative vases at ₹2650 per piece. One of the pieces was slightly damaged. She decides to sell it at a loss of 18%.

Q. Try making an estimate. Draw a rough diagram depicting the given situation.

Due to heavy rains, Snehal could not transport strawberries to Hyderabad from his farm in Panchgani. He sells some of his stock at ₹80 per kg with a 12% loss. What is the cost price?

A utensil store is offering a 35% discount on the cooker with an MRP ₹1800. What is the selling price? If the cost price was ₹900, what is the percentage profit made after the sale?

Check if the calculations are correct in the bill shown.

You may share any bills you have at home with the class. Observe the different elements present in the bills. Are there any similarities or differences in these bills?

Suppose we want to know the expression/formula to find the total interest amount gained at the end of the maturity period. What would be the formula for each of the two options?

Tricky Percentages

Would You Rather?

You have won a contest. The organisers offer you two options to choose from: Option A: You deposit ₹100 and you get back ₹300. Option B: You deposit ₹1000 and you get back ₹1500. What is the percentage gain each option gives? You can choose any option only once. Which option would you choose? Why?

A provision store is offering a stock clearance sale. Customers can choose one of the two options — 20% discount or ₹50 discount—for any purchase above ₹150. Which option would you choose if you want to:

(i) buy items worth ₹180 (ii) buy items worth ₹225 (iii) buy items worth ₹300

Ariba and Arun have some marbles. Ariba says, “The number of marbles with me is 120% of the marbles Arun has”. What would be an appropriate statement Arun could make comparing the number of marbles he has with Ariba’s?