Question

I have a total of 300 coins of denomination Rs1, Rs2and Rs5.The number of 2coins is 3 times the number of Rs5coins. The total number of coins is 160. How many coins of each denomination are with me?

Answer 1

Solution: 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

After dividing both sides by 7, we get

140/7 = 7m/7

=> 140/7 = m

=> m = 20

Thus, number of coins of Rs 5 = 20
Now, since, number of coins of Re 1 = 160 – 4m
Thus, by substituting the value of m, we get
Number of coins of Re 1 = 160 – (4 x 20) = 160 – 80 = 80
Now, number coins of Rs 2 = 3m

Thus, by substituting the value of m, we get
Number of coins of Rs 2 = 3m = 3 x 20 = 60
Therefore,
Number of coins of Re 1 = 80
Number of coins of Rs 2 = 60
Number of coins of Rs 5 = 20