Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Ratio problems with algebra

Forming equations from ratio statements.

14 original questions, 55 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

a and b are two numbers in the ratio a : b = 3 : 5

b − a = 12

Work out the value of a and the value of b.

3 marks
Show answer
a) 18 b) 30
2

The ratio x : (x + 4) is equal to 3 : 5

Work out the value of x.

3 marks
Show answer
x = 6
3

A bag contains only red, blue and yellow counters.

The numbers of red, blue and yellow counters are in the ratio 2 : 3 : x.

A counter is taken at random from the bag.

The probability that it is yellow is 27.

Work out the value of x.

3 marks
Show answer
2
4

A jar contains only red sweets and green sweets.

The ratio of the number of red sweets to the number of green sweets is 4 : 3.

Show that the total number of sweets in the jar must be a multiple of 7.

3 marks
Show answer
Red = 4n and green = 3n for some whole number n, so total = 7n, a multiple of 7
5

Zainab, Yusuf and Ola share £720 in the ratio 5 : 3 : 4

  1. Work out how much Zainab gets.
  2. Yusuf gives one third of his share to Ola. Write down the new ratio of the amounts that Zainab, Yusuf and Ola have, in its simplest form.
  3. Work out the new amount that Ola has as a percentage of the £720. Give your answer correct to 1 decimal place.
5 marks
Show answer
a) £300 b) 5 : 2 : 5 c) 41.7%
6

The ratio (2x + 1) : (x + 5) is equal to 3 : 2

Work out the value of x.

3 marks
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x = 13
7

The ratio of the amount of money Amy has to the amount Ben has is 5 : 3.

Amy gives Ben £14.

The ratio of the amount Amy has to the amount Ben has is now 6 : 5.

Work out how much money Amy had at first.

4 marks
Show answer
£110
8

The ages of a mother and her daughter are in the ratio 7 : 2

In 5 years' time, the ratio of their ages will be 8 : 3

Work out how old the mother and daughter are now.

4 marks
Show answer
a) 35 b) 10
9

The cost of a pencil and the cost of a ruler are in the ratio 2 : 5.

Priti buys 3 pencils and 2 rulers for a total of £3.20.

Work out the cost of a ruler.

4 marks
Show answer
£1
10

The ratio of the amount of money Priya has to the amount of money Quinn has is 7 : 5.

Priya gives Quinn £18.

Now they each have the same amount of money.

Work out how much money Priya had originally.

4 marks
Show answer
£126
11

A box contains red counters and blue counters.

If 5 more red counters are put in the box, the ratio of red to blue will be 2 : 3.

If instead 5 more blue counters are put in the box, the ratio of red to blue will be 1 : 2.

Work out how many counters of each colour are in the box.

5 marks
Show answer
a) 25 red b) 45 blue
12

a and b are positive numbers such that

a2 + 6b2 = 5ab

Find the possible values of the ratio a : b.

5 marks
Show answer
a : b = 2 : 1 or a : b = 3 : 1
13

A box contains only red counters, blue counters and green counters.

The number of blue counters is twice the number of red counters.

The number of green counters is 9 more than the number of red counters.

There are 49 counters in the box altogether.

Work out the ratio of red counters to green counters. Give your answer in its simplest form.

5 marks
Show answer
10 : 19
14

In a box, the ratio of the number of red counters to the number of blue counters is 4 : 7.

12 more red counters are put into the box.

The ratio of the number of red counters to the number of blue counters is now 2 : 3.

Work out the number of blue counters in the box.

4 marks
Show answer
126

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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