Ex.3. In an examination, 60% of the...
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Ex.3. In an examination, 60% of the candidates passed in English and 70% of the candidates passed in Mathematics, but 20% failed in both of these subjects. If 2500 candidates passed in both the subjects, the number of candidates that ap- peared at the examination was (1) 3000 (2) 3500 (3) 4000 (4) 5000

11th - 12th Class
Maths
Solution
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Sol. (4) Let the total number of candidates ( =x ) ( therefore ) Number of candidates passed in English ( =0.6 x ) Number of candidates passed in Maths ( =0.7 x ) Number of candidates failed in both subjects = ( 0.2 x ) Number of candidates passed in atleast one subject ( =x-0.2 x=0.8 x ) ( therefore 0.6 x+0.7 x-2500=0.8 x ) ( Rightarrow 1.3 x-0.8 x=2500 Rightarrow 0.5 x=2500 ) ( Rightarrow x=frac{2500}{0.5}=5000 )
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