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

The total sum of money = ₹300

Let the number of 5 coins be x, the number of 2 coins be 3x and the number of ₹1 coin be $160-\left(x+3x\right)=160-4x$

According to the question, $5\times x+2\times\left(3x\right)+1\times\left(160-4x\right)=300$

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

$\Rightarrow\ 7x+160=300$

$\Rightarrow7x+160-160=300-160$

[Subtracting 160 from both sides]

$\Rightarrow\ 7x=140$

$\Rightarrow\ \frac{7x}{7}=\frac{140}{7}$

[Dividing both sides by 7]

x = 20

Hence, the number of coins of ₹5 denomination = 20

Number of coins of ₹2 denomination = 3 x 20 = 60

Number of coins of ₹1 denomination = 160 - 4 x 20 = 160 - 80 = 80