Question

Rs. 69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy received twice the paise as each girl received. The number of girls in the class is:

Answer 1

Given that $Rs.69$ are divided among a total of $115$ students.

Each girl gets $50paise$ less than a boy.

To find out: Number of girls in the class.

Let the number of boys be $x$ and the number of girls be $y$.

Hence, $x+y=115.....\left(i\right)$

Let the amount received by each boy be $bpaise$.

Hence, amount received by each girl will be $(b-50)paise$.

It is also given that a boy receives twice the paise as each girl.

Hence, $b=2(b-50)$

$\Rightarrow b=2b-100$

$\therefore b=100paise$ and $b-50=100-50=50paise$.

Hence, each boy receives $100paise$, while each girl receives $50paise$.

Total amount $=Rs.69=6900paise$

$\therefore 100\times x+50\times y=6900$

$\Rightarrow 100x+50y=6900$

$\Rightarrow 2x+y=138.....\left(ii\right)$

Subtracting $\left(ii\right)$ from $2\times \left(i\right)$, we get:

$2[x+y=115]-[2x+y=138]$

$\Rightarrow (2x+2y=230)-(2x+y=138)$

$\Rightarrow 2x+2y-2x-y=230-138$

$\Rightarrow y=92$

Hence, the number of girls in the class is $92$.