How to Share an Amount in a Ratio

To share an amount in a ratio, add the parts of the ratio together, divide the amount by that total to find the value of one part, then multiply each part of the ratio by that value. To share £200 in the ratio 3:2, add 3 + 2 = 5 parts, so one part is £200 ÷ 5 = £40. The shares are 3 × £40 = £120 and 2 × £40 = £80. Check that they add back to the amount you started with: £120 + £80 = £200.

Sharing in a ratio is one of the most common question types in employer tests, usually presented as a budget, a staffing split or a share of profit. You can practise it in a free numerical reasoning test.

How to share in a ratio, step by step

Sharing an amount in a ratio means splitting it into equal parts, then handing those parts out in the amounts the ratio describes. The same three steps work for a ratio with two parts, three parts or more.

Example. A company employs 49 staff, with men and women in the ratio 2:5. How many men and how many women are there?

1. Add the parts of the ratio. 2 + 5 = 7. The 49 staff are being split into 7 equal parts.
2. Divide the amount by the total number of parts. 49 ÷ 7 = 7. Each part is worth 7 people.
3. Multiply each part of the ratio by the value of one part. Men: 2 × 7 = 14. Women: 5 × 7 = 35.

Then check: 14 + 35 = 49. If the shares do not add back to the original amount, something has gone wrong.

Worked examples

Example 1: splitting a budget

Mo has £1,500 to spend on clothes for a new job and an armchair for his flat. He splits the money in the ratio 2:3, armchair to clothes. How much is his armchair budget?

1. Add the parts: 2 + 3 = 5.
2. Find one part: £1,500 ÷ 5 = £300.
3. The armchair takes 2 parts: 2 × £300 = £600. The clothes take 3 parts: 3 × £300 = £900.

Check: £600 + £900 = £1,500. The armchair budget is £600.

Example 2: a three-part ratio

Harriet is splitting a £3,900 bonus pot between three staff in the ratio 1:2:3, with the newest member of staff receiving the smallest share. How much does each person get?

1. Add the parts: 1 + 2 + 3 = 6.
2. Find one part: £3,900 ÷ 6 = £650.
3. Multiply: 1 × £650 = £650, 2 × £650 = £1,300 and 3 × £650 = £1,950.

Check: £650 + £1,300 + £1,950 = £3,900.

Example 3: dividing hours between contractors

A project needs 84 hours of work, shared between two contractors in the ratio 3:4. How many hours does each one work?

1. Add the parts: 3 + 4 = 7.
2. Find one part: 84 ÷ 7 = 12 hours.
3. Multiply: 3 × 12 = 36 hours and 4 × 12 = 48 hours.

Check: 36 + 48 = 84.

When you know one share, not the total

Sometimes the question gives you one share and asks for another, or for the total. Use the share you know to find the value of one part.

Example. A recipe uses flour and butter in the ratio 5:2. You have weighed out 350g of flour. How much butter do you need, and how much will the mixture weigh?

1. Flour is 5 parts, so one part is 350g ÷ 5 = 70g.
2. Butter is 2 parts: 2 × 70g = 140g.
3. The whole mixture is 5 + 2 = 7 parts: 7 × 70g = 490g.

Check: 350g + 140g = 490g.

When you know the difference between two shares

Another common version tells you how much more one person gets than another.

Example. Anna and Ben share some money in the ratio 5:3. Anna gets £40 more than Ben. How much money was shared?

1. The difference between the shares is 5 − 3 = 2 parts.
2. Those 2 parts are worth £40, so one part is £40 ÷ 2 = £20.
3. The total is 5 + 3 = 8 parts: 8 × £20 = £160.

Anna gets 5 × £20 = £100 and Ben gets 3 × £20 = £60. Check: £100 − £60 = £40, and £100 + £60 = £160.

Using fractions instead

Each share is the same as a fraction of the total, with the ratio part on top and the sum of the parts underneath. In the ratio 3:2, the first share is 3/5 of the total and the second is 2/5. So 3/5 of £200 is £120, which matches the first example on this page. This route is quicker when you only need one of the shares. Our guide to converting a ratio into a fraction explains it in more detail.

Simplify first if it helps

If the ratio is large, simplifying it first makes the arithmetic easier and does not change the answer. Sharing £900 in the ratio 20:40 is the same as sharing it in 1:2, which gives £300 and £600. There is a full method in our guide on how to simplify ratios.

When the shares do not come out whole

If the amount does not divide exactly, round each share sensibly and check the total. Sharing £1,000 in the ratio 1:2 gives one part of £1,000 ÷ 3 = £333.33 (to the nearest penny). The shares are £333.33 and £666.67, which add back to £1,000.00. With people or items, which cannot be split, a share that is not a whole number usually means you have used the wrong ratio or the wrong total.

Common mistakes to avoid

• Dividing by one part instead of the total. Sharing £200 in the ratio 3:2 means dividing by 5, never by 3.
• Matching the shares to the wrong side. Read carefully which quantity the question names first.
• Confusing a ratio with a fraction. A ratio of 1:2 does not mean one half. The first share is 1/3 of the total. Our guide to ratio vs proportion explains why.
• Skipping the check. Adding the shares back up should return the original amount every time.

Practise sharing in a ratio

In a real assessment the method needs to be automatic, because the pressure comes from the clock rather than the arithmetic. Work through a timed numerical reasoning practice test to see ratio questions in the context of tables and charts.