In an examination, 30% of the candidates failed in English, 35% failed in G.K. and 27% failed in both the subjects. If 310 candidates passed in both, how many candidates appeared in the examination?

Dear Student,

Please find below the solution to the asked query:

Given : In a examination 30% students failed in English and 27 % failed in English and G.K. , So

Percentage of students failed only in English = 30%  - 27%  =  3 %

Also given : In a examination 35% students failed in G.K. and 27 % failed in English and G.K. , So

Percentage of students failed only in G.K. = 35%  - 27%  =  8 %

Then,

Percentage of students failed in one or both subjects = 3 %  + 8 %  + 27 %  = 38 %

So,

Percentage of students passed only in both subjects = 100%  - 38%  =  62 %

Also given : Total students passed in both subjects =  310 , We assume total students appeared for examination = x , So

62 % of x  = 310
$$\begin{gathered} \frac{62 \times x}{100} =310 \\ \Rightarrow x =310\times \frac{100}{62} \\ \Rightarrow x =10\times \frac{{\displaystyle 100}}{{\displaystyle 2}} \\ \Rightarrow x =10\times 50 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{500} \end{gathered}$$
Therefore,

Total students appeared for examination = 500                                                ( Ans )


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