Question

When a bus started from the first stop, the number of male passengers to the number of female passengers was $3:1$. At the first stop, $16$ passengers got down and $6$ more female passengers got in. The ratio of the male to female passengers now became $2:1$. What was the total number of passengers in the bus when it started from the first stop?

Answer 1

Let the number of boys be $3x$

Let the number of girls be $x$

when 16 passengers got down from total & 6 girls got in

$\therefore 3x-16\times \left(\frac{3}{4}\right)\&x-16\times \left(\frac{1}{4}\right)+6$

$\downarrow$ $\downarrow$

Ratio of boys Ratio of girls

$3x-12$ & $x+2$

$\therefore$ New Ratio is $2:1$

$3x-21:x+2::2:1$

$3x-12=2x+4$

$x=16$

$\therefore$ Boys $=3x=48$

Girls $\underset{–}{=x=16}$

$64$