11+ Entrance Maths: Fractions and Percentages Questions and Answers — 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?
- 120
- 90
- 210
- 90 (Correct answer)
Correct answer: 90
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?
- £230
- £200 (Correct answer)
- £50
- £225
Correct answer: £200
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)?
- 0.65, 2/3, 70% (Correct answer)
- 2/3, 0.65, 70%
- 70%, 2/3, 0.65
- 0.65, 70%, 2/3
Correct answer: 0.65, 2/3, 70%
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?
- 280
- 165
- 320 (Correct answer)
- 45
Correct answer: 320
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)?
- 200ml
- 150ml
- 300ml
- 100ml (Correct answer)
Correct answer: 100ml
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.
Question 6: Last year, a train ticket cost £60. This year, the price has increased by 15%. What is the new price of the train ticket?
- £69.00 (Correct answer)
- £75.00
- £60.15
- £72.50
Correct answer: £69.00
To find the price increase, we need to calculate 15% of £60. A good way to do this is to find 10% and 5%. 10% of £60 is £6. 5% is half of 10%, so 5% of £60 is £3. The total increase is 10% + 5% = £6 + £3 = £9. The new price is the original price plus the increase: £60 + £9 = £69.00.
11+ Entrance Maths: Fractions and Percentages Questions and Answers
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?