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  4. 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 Hindi?

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Q. 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 Hindi?

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Solution:

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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 $g = 35$
$n(H) = b + c + e + f = 18$