In an examination, 75% of the candidates passed in English, 65% passed in Mathematics and 8% failed in both. If 96 candidates passed in both subjects, how many candidates took the examination?

128Correct answerYour answer200Correct answerYour answer240Correct answerYour answer300Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Passed in at least one $= 100\% - 8\% = 92\%$ .
Passed in both $= 75\% + 65\% - 92\% = 48\%$ .
48% of the total is 96, so total $= \frac{96 \times 100}{48} = 200$ .

Worth noting

240 takes 'both' as $75\% + 65\% - 100\% = 40\%$ , ignoring the 8% who failed both; 300 subtracts the 8% instead of allowing for it (32%). 128 divides 96 by 75%, as if 96 were the English passes.

Concept: Working back from a percentage overlap
Typical timeTypical: 130 s
Your timeYours: —

The rule this testsCounting with overlapping sets

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Ten questions from Venn Diagrams, at your own pace.

In an examination, 75% of the candidates passed in English, 65% passed in Mathematics and 8% failed in both. If 96 candidates passed in both subjects, how many candidates took the examination?

Explanation