Question

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

• A. Number of $10$ paise coins are $60$ Number of $50$ paise coins are $20$
• B. Number of $10$ paise coins are $20$
  Number of $50$ paise coins are $40$
• C. Number of $10$ paise coins are $40$
  Number of $50$ paise coins are $30$
• D. Number of $10$ paise coins are $30$
  Number of $50$ paise coins are $50$

Answer 1

The correct option is C Number of $10$ paise coins are $40$

Number of $50$ paise coins are $30$
Suppose the number of $10$ paise coins $=x$

$\therefore$ the number of $50$ paise coins $=70-x$

Now, value of $10$ paise coins $=$ Rs. $\frac{x}{10}$

and value of $50$ paise coins $=$ Rs. $\frac{70-x}{2}$

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

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

Multiplying both sides by $10$, (LCM of $10,2=10$), we get

$x+5(70-x)=19\times 10$

$x+350-5x=190$

$-4x=-160$

$\frac{-4x}{-4}=\frac{-160}{-4}$

$\therefore x=40$

$\therefore$ number of $10$ paise coins $=40$

Number of $50$ paise coins $=70-40=30$.