Question

A purse has only one-rupee and two-rupee coins in it. The number of two-rupee coins is one-third the number of one-rupee coins. If the purse has Rs. $115$, find the number of two-rupee coins.

Answer 1

Let the number of $Re.1$ coin be $x$ and

the number of $Rs.2$ coin be $y$.

It is given that the number of two-rupee coins is one-third the number of one-rupee coins.

$\therefore y=\frac{1}{3}x$

$\Rightarrow x=3y$

And, the total money in the purse $=Rs.115$

$1\times x+2\times y=115$

$\Rightarrow x+2y=115$

$\Rightarrow 3y+2y=115$ [From above, $x=3y$]

$\Rightarrow 5y=115$

So, $y=\frac{115}{5}=23$

thus, $x=3y=3\times 23=69$

Hence, there are $69$ one rupee coins and $23$ two rupee coins.