| 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. [SSC (CPO) 2014] |
A) 492
B) 300
C) 500
D) 400
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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