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Class 8 Maths: Fractions in Disguise (Percentages), 8 practice questions with answers

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These are 8 practice questions on Chapter 1, Fractions in Disguise, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover a mistake in turning a fraction into a percentage, what is left of a whole, finding the whole from a part, why a rise and the fall back are different percentages, profit and the least sales that avoid a loss, whether the order of a discount and GST matters, working back from a compounded amount and comparing it with simple interest, and percentage points. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 2, Chapter 1, printed pages 1 to 31):

Fractions, parts and wholes

Question 1. Rohan writes the fraction 7/32 as 7.32%. Kavya says it is a little less than a quarter. Who is closer? Find the exact percentage.

Answer: Kavya; 7/32 = 21.875%. To write a fraction as a percentage, multiply it by 100: 7/32 × 100 = 700/32 = 21.875%. A quarter is 1/4 = 8/32, so 7/32 is a little less than a quarter, as Kavya says. Rohan just wrote the two numbers side by side with a point; 7.32% would be 7.32/100, which is much smaller than 7/32. (Fractions as percentages, pages 1 to 3.)

Question 2. A school's water tank holds 1,750 litres and is 68% full. How many more litres will fill it?

Answer: 560 litres. The tank is 68% full, so 100% − 68% = 32% of it is empty. 32% of 1,750 = 32/100 × 1,750 = 560 litres. Check: 68% of 1,750 is 1,190 litres, and 1,190 + 560 = 1,750. (Percentage of some quantity, pages 6 and 7.)

Question 3. A library has 399 Hindi books, which is 57% of all its books. Sohan works out the total as 399 + 57% of 399 = 626.43. Find his mistake, and give the right total and the number of books that are not in Hindi.

Answer: 700 books in all; 301 are not in Hindi. The 57% is a part of the total, not of 399, so 57/100 × total = 399, and total = 399 × 100 ÷ 57 = 700. Sohan took 57% of the wrong quantity (and a library cannot have 0.43 of a book). The other books are 700 − 399 = 301. (Finding the whole when a percentage of it is known, page 10.)

Changes, profit and prices

Question 4. A cricket club's members went up from 325 to 507 in one year, a rise of 56%. The next year they went back down to 325. Jai says that is a fall of 56%. Is he right?

Answer: no; the fall is about 35.9%. Both changes are 182 members (507 − 325), but a percentage change is worked out on the original amount. The rise is 182 ÷ 325 × 100 = 56%. The fall starts from 507, so it is 182 ÷ 507 × 100 ≈ 35.9%. The same number of members is a smaller share of the bigger total. (Percentage increase or decrease, pages 15 and 16.)

Question 5. A sweet shop makes 77 boxes of laddoos at a cost of ₹128 a box and sells each box for ₹184. What is its profit percentage if it sells every box? What is the least number of boxes it must sell so that it makes no loss?

Answer: 43.75%; at least 54 boxes. The profit on a box is ₹184 − ₹128 = ₹56, and the profit percentage, on the cost price, is 56/128 × 100 = 43.75%. All 77 boxes cost 77 × 128 = ₹9,856 to make. Selling 53 boxes brings in 53 × 184 = ₹9,752, less than the cost; selling 54 brings in 54 × 184 = ₹9,936, more than the cost. So the shop must sell at least 54 boxes. (Profit and percentage profit on the cost price, pages 16 and 17.)

Question 6. A jacket is marked ₹1,450. The shop gives an 8% discount, and 5% GST is added. Does it matter whether the discount is taken off before the GST is added, or after? What does the customer pay?

Answer: no; ₹1,400.70 either way. Discount first: 8% of 1,450 is ₹116, so the price is ₹1,334; 5% GST on that is ₹66.70, so the customer pays ₹1,400.70. GST first: 5% of 1,450 is ₹72.50, so ₹1,522.50; 8% off that is ₹121.80, leaving ₹1,400.70. Each step multiplies the price by a number (0.92 for the discount and 1 + 5/100 for the GST), and the order of multiplication does not change the answer. (Discounts, page 18; GST, page 19; changes applied one after another multiply, page 26.)

Compounding and percentage points

Question 7. Meena put some money in a fixed deposit at 8% per year, compounded every year. After 2 years she received ₹10,206. How much did she deposit? What yearly interest rate, without compounding, would have given her the same ₹10,206 after 2 years?

Answer: ₹8,750; 8.32% a year. With compounding, the deposit is multiplied by 1.08 each year, so deposit × 1.08 × 1.08 = 10,206. Working back: 10,206 ÷ 1.08 = 9,450, and 9,450 ÷ 1.08 = 8,750. Without compounding, the interest is the same every year. She gained 10,206 − 8,750 = ₹1,456 in 2 years, which is ₹728 a year, and 728 ÷ 8,750 × 100 = 8.32%. So 8% compounded every year does as well as 8.32% without compounding over 2 years. (Growth and compounding, pages 20 to 23.)

Question 8. In a village, the share of homes with a tap connection rose from 32% to 76%. A newspaper writes that it "rose by 44%". What is the right way to describe the rise?

Answer: it rose by 44 percentage points, which is a 137.5% increase. 76% − 32% = 44 is a difference between two percentages, so it is 44 percentage points. The percentage increase is worked out on the original share: 44 ÷ 32 × 100 = 137.5%, so the share is more than double what it was. "Rose by 44%" would mean the share grew by 44% of 32%, to only 1.44 × 32% = about 46.1%, which is not what happened. (Percentage increase, pages 15 and 16.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.