Question

I have a total of Rs. $300$ in coins of denomination Re. $1$, Rs. $2$ and Rs. $5$. The number of Rs. $2$ coins is $3$ times the number of Rs. $5$ coins. The total number of coins is $160$. How many coins of each denomination are with me?

• A. Number of Re. $1$ coins $=50$; Number of Rs. $2$ coins $=40$; Number of Rs. $5$ coins $=40$
• B. Number of Re. $1$ coins $=70$; Number of Rs. $2$ coins $=70$; Number of Rs. $5$ coins $=19$
• C. Number of Re. $1$ coins $=80$; Number of Rs. $2$ coins $=60$; Number of Rs. $5$ coins $=20$
• D. Number of Re. $1$ coins $=115$; Number of Rs. $2$ coins $=50$; Number of Rs. $5$ coins $=15$

Answer 1

The correct option is C Number of Re. $1$ coins $=80$; Number of Rs. $2$ coins $=60$; Number of Rs. $5$ coins $=20$

Given, Total number of coins $=160$

Given that the number of Rs.$2$ coins are $3$ times the number of Rs. $5$ coins.

Number of Rs. $5$ coins $=x$

Number of Rs. $2$ coins $=3x$

Number of Re. $1$ coins $=160-(x+3x)=160-4x$

Total value of coins $=$ Rs. $300$

So, $5\times x+2\times 3x+1\times (160-4x)=300$

$5x+6x+160-4x=300$

$7x=140$

$x=20$

So, number of Rs. $5$ coins $=20$

Number of Rs. $2$ coins $=60$

Number of Re. $1$ coins $=80$