SATHEE: Quantitative Aptitude Ques 1355

Quantitative Aptitude Ques 1355

Question: In an examination, 75% candidates passed in English and 60% passed in Mathematics. 25% failed in both and 240 passed the examination. Find the total number of candidates.

Options:

A) 492

B) 300

C) 500

D) 400

Show Answer

Answer:

Correct Answer: D

Solution:

Let the total number of candidates be x. Number of candidates passed in English, $ =n(E)=75% $ Number of candidates passed in Maths, $ =n(M)=60% $ Now, number of candidates passed either in English in Maths or in both $ =n(E\cup M)=(100-25)=75% $ Number of candidates passed in both subjects i.e. passed the exam $ =n[E\cap M] $ We know that, $ =n(E\cap M)=n(E)+n(M)-n(E\cap M) $ $ 75=60+75-n(E\cap M) $ $ n(E\cap M)=60% $ Now, given total candidates passed $ =240 $

$ \therefore $ 60% of $ x=240 $

$ \Rightarrow $ $ \frac{60}{100}\times x=240 $

$ \Rightarrow $ $ x=\frac{240\times 100}{60} $

$ \Rightarrow $ $ x=400 $

$ \therefore $ Total number of candidates $ =400 $

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