I have a total of 300 $ in coins of denomination 1 $, 2 $,5$. 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 denominations are with me?

The ratio of $2 to $5 is 3: 1

3x$2 + 1x$5 = $11

A set of 3 $2 and 1 $5 gives you $11.

Assumed all 160 coins are $1

Total value = $100

Difference in the value = $300 - $100 = $200

Difference in the $1 and the set of $2 and $5 = $11 - $1 = $10

Number of set of $2 and $5 = $200 : $10 = 20

Calculate the number of $2 and $5 in the 20 sets:

Number of $2 = 3 x 20 = 60

Number of $5 = 1 x 20 = 20

Number of $1 = 160 - 60 - 20 = 80

Answer: There are 80 $1, 60 $2 and 20 $5.