In a mathematics class, 20 children had forgotten their ruler and 17 had forgotten their pencil. The teacher asked them to go and borrow from their friends. If 24 children left the room, then the number of children who had forgotten both rulers and pencil are ______.

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Solution

The correct option is C 13
Let R be the set of children who forgot ruler, and P be the set of children who forgot pencil.
Then, the intersection of the two sets represent the children who forgot both rulers and pencil. Let $R \cap P$ be x.

Total number of children who left the room, that is $R \cup P$ , = 24
So, number of children in only set R $= n (R) - n (R \cap P) = 20 - x$
And, number of children in only set P $= n (P) - n (R \cap P) = 17 - x$
So, $n (R \cup P)$ = 24 = elements in only R + elements in only P + elements in both R and P
$n (R \cup P)$ = 20 - x + 17 - x + x
24 = 37 – x
x = 13

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