Given, total value of Rs = Rs 300Total number of coins = 160Coins of denomination = Re 1, Rs 2 and Rs 5Number of Rs 2 coins = 3 x number Rs 5 coinsLet the number of coins of Rs 5 = mSince, the number coins of Rs 2 is 3 times of the number of coins of Rs 5Therefore, number of coins of Rs 2=m×3=3mNow, 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 – 4mTotal 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×(160–4m)] + (2×3m) + (5×m)⇒ 300 = (160–4m) + 6m + 5m⇒ 300 = 160 – 4m + 6m + 5m⇒ 300 = 160 – 4m + 11m⇒ 300 = 160 + 7mAfter transposing 160 to LHS, we get300 – 160 = 7m⇒ 140 = 7mAfter dividing both sides by 7, we get 1407 = 7m7Or, m = 20Thus, number of coins of Rs 5 = 20Now, since, number of coins of Re 1=160–4mThus, by substituting the value of m, we getNumber of coins of Re 1= 160 – (4×20) = 160 – 80 = 80Now, number coins of Rs 2 = 3mThus, by substituting the value of m, we getNumber of coins of Rs 2= 3m = 3×20 = 60Therefore,Number of coins of Re 1 = 80Number of coins of Rs 2 = 60Number of coins of Rs 5 = 20

any short method