Ratio and share questions

Numerical reasoning practice > Ratio and share questions

Ratio questions are short and are failed for one reason: putting the wrong value on the bottom. The wording tells you which, and the wording is easy to skim past.

1. Which value goes on the bottom

"A is how many times B" means A ÷ B. The value after "times" is the denominator.

• "The revenue of D is how many times that of C" → D ÷ C
• "C is what fraction of D" → C ÷ D
• "The ratio of D to C" → D : C, which is D ÷ C expressed as a ratio

Getting this backwards produces the reciprocal, and the reciprocal is always one of the options.

2. Worked example: how many times

The table below shows the annual revenue of each store.

Store A 440   Store D 630   Store B 610   Store C 180
(unit: £000s)

The revenue of Store D is how many times that of Store C?

How to work it

• "D is how many times C" → D on top, C on the bottom
• 630 ÷ 180
• Both divide by 90: 7 ÷ 2 = 3.5 times

Simplifying before dividing is faster than reaching for long division, and it is the step that makes these doable in the time allowed.

3. Share of a total

A share question needs a denominator you have to build yourself: the total of every row.

• Add all rows to get the total
• Divide the row in question by that total
• Multiply by 100 if a percentage is asked for

The common error is dividing by the largest row instead of the total. If the options include a number above 100%, that error is what the option is there to catch.

4. Ratios given as parts

When a ratio is given as "3 : 5", the total is eight parts, not five. To split £4,000 in the ratio 3 : 5:

• Total parts: 3 + 5 = 8
• One part: 4,000 ÷ 8 = 500
• The shares are 1,500 and 2,500

Always find the value of one part first. Trying to go straight to the answer is where the arithmetic goes wrong.