11+ Entrance Maths: Fractions and Percentages Questions and Answers

Question 1

A library has 300 books. 2/5 of the books are fiction and 30% are non-fiction. The rest are poetry books. How many poetry books are in the library?

Accepted Answer

90

Answer

First, calculate the number of fiction books: 2/5 of 300 is (300 ÷ 5) × 2 = 60 × 2 = 120. Next, calculate the number of non-fiction books: 30% of 300 is (300 ÷ 100) × 30 = 3 × 30 = 90. Add these together: 120 + 90 = 210. Finally, subtract this total from the original number of books to find the number of poetry books: 300 - 210 = 90.

Question 2

A bicycle that normally costs £250 is in a sale with a 20% discount. What is the sale price of the bicycle?

Accepted Answer

£200

Answer

To find the discount amount, calculate 20% of £250. 10% of £250 is £25, so 20% is 2 × £25 = £50. The sale price is the original price minus the discount: £250 - £50 = £200. Alternatively, if there is a 20% discount, you pay 80% of the price. 80% of £250 is 0.8 × 250 = £200.

Question 3

Which of the following lists is in ascending order (smallest to largest)?

Accepted Answer

0.65, 2/3, 70%

Answer

To compare the values, convert them all to the same format, such as percentages. 0.65 is 65%. 2/3 is approximately 66.7% (since 1/3 is 33.3...). 70% is already a percentage. Therefore, the correct order from smallest to largest is 65% (0.65), 66.7% (2/3), and then 70%.

Question 4

At a school fête, 3/8 of the attendees are children. If there are 120 children at the fête, how many attendees are there in total?

Accepted Answer

320

Answer

If 3/8 of the total attendees is equal to 120 children, we first need to find the value of 1/8. To do this, we divide 120 by 3, which gives us 40. This means 1/8 of the total is 40 people. To find the total number of attendees (which is 8/8), we multiply 40 by 8. 40 × 8 = 320. So, there are 320 attendees in total.

Question 5

A recipe for a fruit smoothie requires 400ml of juice. 50% of the juice is apple juice and 1/4 is orange juice. The rest is mango juice. How much mango juice is needed in millilitres (ml)?

Accepted Answer

100ml

Answer

First, calculate the amount of apple juice: 50% of 400ml is 200ml. Next, calculate the amount of orange juice: 1/4 of 400ml is 100ml. The total amount of apple and orange juice is 200ml + 100ml = 300ml. The rest is mango juice, so subtract this from the total: 400ml - 300ml = 100ml.

11+ Practice Test

11+ Practice Test

11+ Entrance Maths: Fractions and Percentages Questions and Answers