Question

A man has only $20$ paisa coins and $25$ paisa coins in his purse. If he has $50$ coins in all totaling Rs. $11.25$, how many coins of each kind does he have?

Answer 1

Let the number of $20$ paisa coins be $x$ and that of $25$ paisa coins be $y$. Then,
$x+y=50$ (i)

Total value of $20$ paisa coins $=20x$ paisa

Total value of $25$ paisa coins $=25y$ paisa

$\therefore 20x+25y=1125$ { $100$ Paisa = $1$Rs.}

$\Rightarrow 4x+5y=225$ (ii)

Thus, we get the following system of linear equations

$x+y-50=0$

$4x+5y-225=0$

By using cross-multiplication, we have

$\frac{x}{-225+250}=\frac{-y}{-225+200}=\frac{1}{5-4}$

$\Rightarrow \frac{x}{25}=\frac{y}{25}=\frac{1}{1}\Rightarrow x=25$ and $y=25$

Hence, there are $25$ coins of each kind.