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Question
Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave `1/3` of her money to Aarushi as her birthday gift. Then Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs.1600, find the sum gifted by Anushka.
Solution
Let Anushka and Aarushi have equal amount of money in their pocket, which is ₹ x.
After giving `1/3` of the money of Anushka to Aarushi,
Amount of Aarushi = `₹ (x + x/3)`
According to the question,
`(x + x/3) - 1/2 xx (x + x/3) = 1600`
⇒ `(x + x/3)(1 - 1/2) = 1600`
⇒ `(x + x/3)xx 1/2 = 1600`
⇒ `(3x + x)/3 = 1600 xx 2`
⇒ `(4x)/3 = 3200`
∴ `x = 3200 xx 3/4 = 2400`
So, money gifted by Anushka = `1/3` of 2400
= `1/3 xx 2400`
= ₹ 800
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