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. 

Answer 1

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