Question

A change making machine contains $1$ rupee, $2$ rupee and $5$ rupee coins. The total number of coins is $300$. The amount is Rs $960$ if the number of $1$ rupee coins and the number of $2$ rupee coins are interchanged, the value comes down by Rs. $40$. The total number of $5$ rupee coins is:

• A. $100$
• B. $140$
• C. $60$
• D. $150$

Answer 1

Answer: (B)

$140$

Let $1$ rupee coins $=x$
$2$ rupee coins $=y$
$3$ rupee coins $=z$
Then, $x+y+z=300$ ......... $\left(1\right)$
and, $x+2y+5z=960$ ........ $\left(2\right)$
also, $y+2x+5z=920$ ......... $\left(3\right)$
Add (1) and (2) and subtract 3 times the equation (1)
$3x+3y+10z-3x-3y-3z=960+920-900$
$7z=980$
$z=140$
Thus, $5$ rupee coins are $140$ in number.