Question

In a survey of $100$ students, the number of students studying the various languages were found to be : English only $18$, English but not Hindi $23$, English and Sanskrit $8$, English $26$, Sanskrit $48$, Sanskrit and Hindi $8$, no language $24$. Find How many students were studying English and Hindi?

• A. $2$
• B. $5$
• C. $4$
• D. $3$

Answer 1

Answer: (D)

$3$

Answer 2

We have, $a = 18$, $a + d = 23$, $d + e = 8$, $a + b + d+ e = 26$, $d + e + f + g = 48$, $e + f= 8$, $a + b + c + d + e + f + g$ $= 100 - 24 = 76$ $\therefore a = 18$, $b = 0$, $c= 10$, $d = 5$, $e = 3$, $f = 5$ and $g = 35$ $n (H \cap E) = b + e = 3$