Question

In a class the ratio of the number of boys to that of the girls is $7:3$. Each boy is given only a $50$ paise coin and each girl is given a $75$ paise coin (assuming $75$ paise coins are available) The difference in the amount present with the boys and the girls is Rs. $3.75$. How many coins should the boys and girls exchange so that the amount with the boys becomes twice the amount with the girls?

• A. $8$
• B. $6$
• C. $4$
• D. $9$

Answer 1

Answer: (C)

$4$

Solution:

Let us suppose number of boys $=7x$

and number of girls$=3x$

Now,

$7x\left(0.5\right)-3x\left(0.75\right)=3.75$

or, $14x-9x=15$

or, $x=3$

So, number of boys $=7x=7\times 3=21$

and number of girls $=3x=3\times 3=9$

Let $y$ of them exchange coins

then

$0.5\times (21-y)+0.75y=2[0.75\times (9-y)+0.5y]$

or, $42-2y+3y=54-6y+4y$

or, $3y=12$

or, $y=4$

So, number of coins boys and girls should exchange $=4$

Hence, C is the correct answer.