Question

A purse contains only 25 paise and 10 paise coins. The total amount in the purse is Rs. 8.25. If the number of 25 paise coins is one-third the number of 10 paise coins, then the total number of coins in the purse is:

Answer 1

Let $x$ be the number of $25$-paise coins and $y$ be the number of $10$-paise coins.

Value of one $25$ paise coin $=Rs.0.25$

Value of one $10$ paise coin $=Rs.0.10$

Given that the total amount in the purse is $Rs.8.25$.

$\therefore 0.25x+0.10y=8.25$

$\Rightarrow \frac{1}{4}x+\frac{1}{100}y=8.25$ ....(1)

Also given that, the number of $25$ paise coins are one-third of $10$ paise coins.

$\therefore x=\frac{1}{3}y$ ....(2)

Substituting (2) in (1), we get:

$\frac{1}{12}y+\frac{1}{100}y=\frac{825}{100}$

$\Rightarrow \frac{112}{1200}y=\frac{825}{100}$

$\Rightarrow y=\frac{825\times 12}{112}$
$\Rightarrow y=45$

Substituting value of $y$ in (2), we get:

$\therefore x=15$

So, the total number of coins $=15+45=60$.

Hence, there are a total of $60$ coins in the purse.