Question

When 40% of the girls left the school assembly, the ratio of the number of boys to girls became 3 to 4. If there were w girls when the assembly started, what was the total number of boys and girls when the assembly started?

Answer 1

Number of girls at the time of the assembly started = w

Number of girls left = 40% of w

$=\frac{40}{100}w$

$=\frac{2}{5}w$

Remaining girls = $w-\frac{2}{5}w$

$=\frac{3}{5}w$

Now, the ratio of the number of boys to girls became 3 to 4.

Let n be the number of boys.

Then, $n:\frac{3}{5} w=3:4$

Or, $\frac{n}{3w/5}= \frac{3}{4}$

$\frac{5n}{3w}= \frac{3}{4}$

20n = 9w

or, n = $\frac{9}{20} w$

Total number of boys and girls = $\frac{9}{20}w+ \frac{3}{5} w$

$= \frac{9}{20}w+ \frac{12}{20} w$

$= = \frac{21}{20}w$

Hence, the total number of boys and girs is $\frac{21}{20} w.$