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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?
A
$16$
B
$24$
C
$30$
D
$36$
(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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