Question

A lady has $25p$ and $50p$ coins in her purse. If in all she has $40$ coins totalling $Rs.12.50$, find the number of coins of each type she has.

• A. $x=40\left(25pcoins\right)$ and $y=15\left(50pcoins\right)$
• B. $x=15\left(25pcoins\right)$ and $y=20\left(50pcoins\right)$
• C. $x=30\left(25pcoins\right)$ and $y=10\left(50pcoins\right)$
• D. $x=10\left(25pcoins\right)$ and $y=30\left(50pcoins\right)$

Answer 1

Answer: (C)

$x=30\left(25pcoins\right)$ and $y=10\left(50pcoins\right)$

Let the number of $50$p coin be $x$ and $25$p be $y$
According to question,
$x+y=40$ (i) and
$25x+50y=1250$ (ii)
Multipling equation (i) by $25$ we get,
$25x+25y=1000$ (iii)
Subtracting (iii) from (ii) we get,
$25x+50y=1250$
$25x+25y=1000$

$25y=250$
$=>y=\frac{250}{25}$
$=>y=10$
Putting the value of $y$ in equation (i) we get,
$x+y=40$
$=>x=40-10$
$=>x=30$
$\therefore x=30$(25 paisa coins)
$y=10$(50 paisa coins)