Question

A bag contains $25$p, $50$p and $1$ rupee coins. There are $220$ coins in all and the total amount in bag is $160$. If there are thrice as many $1$ rupee coins as there are $25$p coins, then what is the no. of $50$ paise coins?

• A. $60$
• B. $40$
• C. $120$
• D. $80$

Answer 1

Answer: (A)

$60$

Let no. of $25$ paise coins be $x$. Then the number of $1$ rupee coins are $3x$
Let the number of $50$ paise coins $=y$
Total number of coins $=220$
Total amount $=$ Rs. $160$
Now,
$0.25x+0.5y+3x=3.25x+0.5y=160...\left(1\right)$

Total number of coins,
$x+3x+y=220$
$4x+y=220...\left(2\right)$
Multiply equation $\left(1\right)$ by $2$ and subtract from equation $\left(2\right)$
$6.5x+y-4x-y=320-220$
$\Rightarrow 2.5x=100$
$\Rightarrow x=40$
Putting the value of $x=40$ in equation $\left(2\right)$
$(4\ast 40)+y=220$
$160+y=220$
$\Rightarrow y=60$
$\therefore$ Number of coins of $50$ paise coins $=60$