I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5.

1.	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?
Answer» Let the number of Rs 5 coins be x. Number of Rs 2 coins = 3 × Number of Rs 5 coins = 3x Number of Re 1 coins = 160 − (Number of coins of Rs 5 and of Rs 2) = 160 − (3x + x) = 160 − 4x Amount of Re 1 coins = Rs [1 × (160 − 4x)] = Rs (160 − 4x) Amount of Rs 2 coins = Rs (2 × 3x)= Rs 6x Amount of Rs 5 coins = Rs (5 × x) = Rs 5x It is given that the total amount is Rs 300. ∴ 160 − 4x + 6x + 5x = 300 160 + 7x = 300 On transposing 160 to R.H.S, we obtain 7x = 300 - 160 7x = 140 On dividing both sides by 7, we obtain 7x/7 = 140/7 x = 20 Number of Re 1 coins = 160 − 4x = 160 − 4 × 20 = 160 − 80 = 80 Number of Rs 2 coins = 3x = 3 × 20 = 60 Number of Rs 5 coins = x = 20

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?

Answer»

Let the number of Rs 5 coins be x.

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

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

= 160 − (3x + x) = 160 − 4x

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

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

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

It is given that the total amount is Rs 300.

∴ 160 − 4x + 6x + 5x = 300 160 + 7x = 300

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

7x = 300 - 160

7x = 140

On dividing both sides by 7, we obtain

7x/7 = 140/7

x = 20

Number of Re 1 coins = 160 − 4x

= 160 − 4 × 20 = 160 − 80 = 80

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

Number of Rs 5 coins = x = 20