Question

$70$coins of $10$ paise and $50$ paise are mixed in a purse. If the total value of the money in the piggy bank is$\mathrm{Rs}.19$, find the number of each type of coins in the piggy bank.

Answer 1

Let the number of $10$ paise coins $=\mathrm{x}$

So, the number of $50$ paise coins$=70–\mathrm{x}$

Value of $10$ paise coins $=\frac{\mathrm{x}}{10}$

Value of $50$ paise coins $=\frac{(70–x)}{2}$

Total value of coins$=\frac{\mathrm{x}}{10}+\frac{70-x}{2}$

$19=\frac{\mathrm{x}}{10}+\frac{70-x}{2}$

$\begin{array}{rcl}\mathrm{x}+5\left(70-\mathrm{x}\right)& =& 19\times 10\\ \mathrm{x}+350-5\mathrm{x}& =& 190\\ -4\mathrm{x}& =& -160\\ \mathrm{x}& =& 40\end{array}$

Hence, the number of $10$ paise coins are $40$ and the number of $50$ paise coins are $30$