In a classroom, one-fifth of boys leave class and ratio of remaining boys to girls is 2: 3 . If furt

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1.Set Theory

hard

In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2: 3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5: 2$. How many more boys should leave the class so that the number of boys equals that of girls?

$16$

$24$

$30$

$36$

(KVPY-2017)

Solution

(b)

Let the number of boys and girls in classroom is $x$ and $y$, respectively. Given, $\frac{x-x / 5}{y}=\frac{2}{3} \Rightarrow \frac{4 x}{5 y}=\frac{2}{3}$

From Eqs.$(i)$ and $(ii)$, we get

$x=50, y=60$

Let $z$ number of boy leaves so number of boys and number of girls are equal.

$\therefore \quad 50-10-z=60-44 z=40-16=24$

Standard 11

Mathematics

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medium

In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2: 3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5: 2$. How many more boys should leave the class so that the number of boys equals that of girls?

Solution

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In a survey of $60$ people, it was found that $25$ people read newspaper $H , 26$ read newspaper $T, 26$ read newspaper $I, 9$ read both $H$ and $I, 11$ read both $H$ and $T,$ $8$ read both $T$ and $1,3$ read all three newspapers. Find:

the number of people who read at least one of the newspapers.