Question

devesh has 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. find number of coins of each denomination​

Answer 1

Answer:

Given, total value of Rs = Rs 300

Total number of coins = 160

Coins of denomination = Re 1, Rs 2 and Rs 5

Number of Rs 2 coins = 3 x number Rs 5 coins

Let the number of coins of Rs 5 = m

Since, the number coins of Rs 2 is 3 times of the number of coins of Rs 5

Therefore, number of coins of Rs 2 = m x 3 = 3m

Now, Number of coins of Re 1 = Total number of coins – (Number of Rs 5 coins + Number of Rs 2 coins)

Therefore,

Number of coins of Re 1 = 160 – (m + 3m) = 160 – 4m

Total Rs = (Re 1 x Number of Re 1 coins) + (Rs 2 x Number of Rs 2 coins) + (Rs 5 x Number of Rs 5 coins)

⇒ 300 = [1 x (160 – 4m)] + (2 x 3m) + (5 x m)

⇒ 300 = (160 – 4m) + 6m + 5m

⇒ 300 = 160 – 4m + 6m + 5m

⇒ 300 = 160 – 4m + 11m

⇒ 300 = 160 + 7m

After transposing 160 to LHS, we get

300 – 160 = 7m

⇒ 140 = 7 m