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Question
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?
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Solution
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 = 140/4`
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
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