Dinesh, Prateek and Ankush go for a party in a restaurant. Dinesh has four times as many coins as Prateek and 9 more than Ankush. When Dinesh gives away 50% of his coins, Prateek and Ankush agree to split those coins up equally. Now, Ankush has twice as many coins as Prateek. How many coins did Prateek start with?
Explanation:
Let Prateek has x coins.
Dinesh has four times as many coins as Prateek i.e., number of coins with Dinesh = 4x.
Dinesh has 9 more coins than Ankush i.e., number of coins with Ankush = 4x – 9
Now, when Dinesh gave 50% i.e., 2x coins, Prateek and Ankush divided them equally among themselves.
∴ Each of them receives x coins and now Ankush has twice the number of coins as Prateek.
∴ (4x - 9 + x) = 2(x + x)
⇒ x = 9
∴ Prateek had 9 coins.
Hence, option (a).
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