Question

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

Answer 1

Given: Total sum of money $=Rs.300$

Total number of coins $=160$

Let the number of $Rs.5$ coins be $x.$
Number of $Rs.2$ coins be $3x$ and
Number of $Rs.1$ coins be $160-(x+3x)=(160-4x)$.

According to question, we have
$5\times x+2\times \left(3x\right)+1\times (160-4x)=300$
$\Rightarrow 5x+6x+160-4x=300$
$\Rightarrow 7x+160=300$
$\Rightarrow 7x+160-160=300-160$ [Subtracting $160$ from both sides]
$\Rightarrow 7x=140$

$\Rightarrow \frac{7x}{7}=\frac{140}{7}$ [Dividing both sides by $7$]
$\Rightarrow x=20$

Hence, the number of coins of $Rs.5$ denomination
$=20$

Number of coins of $Rs.2$ denomination
$=3\times 20=60$

Number of coins of $Rs.1$ denomination
$=160–4\times 20=160–80=80$