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In a class, each student likes either cricket or football, $40 %$ of the students like football, $80 %$ of the students like cricket. The number of students who like only cricket is 40 more than the number of students who like only football. Then the strength of the class is

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100

120

150

answer is B.

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Detailed Solution

Let total strength be $' y'$

$n (C) = 80 % of y = \frac{80 y}{100}$

$n (F) = 40 % of y = \frac{40 y}{100}$

$n (C \cup F) = n (C) + n (F) - n (C \cap F)$

$y = \frac{80 y}{100} + \frac{40 y}{100} - n (C \cap F)$

$\Rightarrow n (C \cap F) = \frac{120 y}{100} - y = \frac{20 y}{100}$

$only C = n (C) - n (C \cap F) = \frac{60 y}{100}$

$only F = n (F) - n (C \cap F) = \frac{20 y}{100}$

By the data $\frac{60 y}{100} - \frac{20 y}{100} = 40$

$\Rightarrow y = 100$

$∴$ Total strength $= 100$

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