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A man has a collection of 10 rupees coins. From his collection, he gave half of the coins to his son. From the remaining coins, he gave half to his daughter. From the remaining coins, he gave 1/4 to his wife. If he is still left with Rs. 630, how many coins were initially there in his collection?

A man has a collection of 10 rupees coins. From his collection, he gave half of the coins to his son. From the remaining coins, he gave half to his daughter. From the remaining coins, he gave 1/4 to his wife. If he is still left with Rs. 630, how many coins were initially there in his collection? Correct Answer 336

Let there were ‘x’ coins in the collection

⇒ No. of coins given to son = x/2

⇒ Remaining coins = x – (x/2) = x/2

⇒ No. of coins given to daughter = (1/2) × (x/2) = x/4

⇒ Remaining coins = (x/2) – (x/4) = x/4

⇒ No. of coins given to wife = (1/4) × (x/4) = x/16

⇒ Remaining coins = (x/4) – (x/16) = 3x/16

But, he is left with Rs. 630,

⇒ No. of coins left = 630/10 = 63

⇒ 3x/16 = 63

⇒ x = (16/3) × 63 = 336

∴ There were 336 coins in the collection

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