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?

Let the
number of Rs 5 coins be *x*.

Number of
Rs 2 coins = 3 × Number of Rs 5 coins = 3*x*

Number of Re 1 coins = 160 − (Number of coins of Rs 5 and of Rs 2)

= 160 − (3*x* + *x*) = 160 − 4*x*

Amount of
Re 1 coins = Rs [1 × (160 − 4*x*)] = Rs (160 −
4*x*)

Amount of Rs 2 coins = Rs (2 × 3*x*)= Rs 6*x*

Amount of
Rs 5 coins = Rs (5 × *x*) = Rs 5*x*

It is given that the total amount is Rs 300.

∴
160 − 4*x* + 6*x* + 5*x* = 300

160 + 7*x*
= 300

On transposing 160 to R.H.S, we obtain

7*x*
= 300 − 160

7*x*
= 140

On dividing both sides by 7, we obtain

*x* =
20

Number of
Re 1 coins = 160 − 4*x* = 160 − 4 × 20 = 160 −
80 = 80

Number of
Rs 2 coins = 3*x* = 3 × 20 = 60

Number of
Rs 5 coins = *x* = 20

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