Question

I have a total of $Rs.300$ in coins of denomination $Rs.1$, $Rs.2$, $Rs.5$. 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?

Answer 1

Let $O,T,F$ be the number of $Rs.1,Rs.2,Rs.5$ coins.

Given that,

$T=3F$ .......$\left(1\right)$

$O+T+F=160$ .........$\left(2\right)$

Substitute $\left(1\right)$ in $\left(2\right)$ we get,

$O+3F+F=160$

$\Rightarrow O+4F=160$

$\Rightarrow O=160-4F$ .....$\left(3\right)$

Also,

$\Rightarrow O+2T+5F=300$

Substitute the values from $\left(1\right)$ and $\left(3\right)$ in the above equation,

$160-4F+2\left(3F\right)+5F=300$

$\Rightarrow 7F=140$

$\Rightarrow F=20$

Thus,

$T=3F$

$\Rightarrow T=3\times 20$

$\Rightarrow T=60$

And,

$O=160-4\left(20\right)$

$\Rightarrow O=80$

So, there are $80$ coins of $Rs.1,$ $60$ coins of $Rs.2$ and $20$ coins of $Rs.5.$