Ratio problems: fractions, 1 : n and changing ratios

Ratio questions are often disguised. Turning a ratio into fractions or into 'one part' unlocks almost all of them.

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Ratios and fractions

In the ratio 3 : 5 there are 8 parts. The first share is 38 of the total.
Comparing the parts: A is 35 of B, and B is 53 of A.
One quantity as a fraction of another: 45 minutes as a fraction of 2 hours is 45120 = 38.

1 : n and the difference

To write 5 : 8 in the form 1 : n, divide both by 5: 1 : 1.6.
If A : B = 3 : 5 and B has £24 more than A, the difference is 2 parts.
One part = 24 ÷ 2 = £12, so A = £36 and B = £60.

Combining and changing ratios

a : b = 2 : 3 and b : c = 4 : 5. Make b the same: 8 : 12 and 12 : 15, so a : b : c = 8 : 12 : 15.
Changing ratio: boys : girls = 3 : 2. 6 more girls join and it becomes 1 : 1.
Boys 3k, girls 2k + 6. 3k = 2k + 6, so k = 6 and there are 18 boys.
Worked example

A : B = 3 : 5. B gets £24 more than A. How much does A get?

  1. The difference is 5 − 3 = 2 parts.
  2. 2 parts = £24, so 1 part = £12.
  3. A = 3 × 12 = £36

Answer: £36

Key idea

Total the parts to get fractions of the whole. Use the difference in parts when a difference is given. Make the shared quantity equal to combine ratios.

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2 more questions

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  1. Write 10 : 15 in the form 1 : n. Find n.

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    Answer: 1.5

    Divide both parts by 10: 1 : 1.5.

  2. Sweets are shared in the ratio 5 : 8. The second person gets 24 more than the first. How many sweets are there altogether?

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    Answer: 104

    Difference = 3 parts = 24, so 1 part = 8. Total = 13 parts = 104.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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