Question

Question 82

Solve the following:

Anushka and Arushi are friends. They have equal amount of money in their pockets. Anushka gave $\frac{1}{3}$ of her money to Arushi as her birthday gift. Then, Arushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Arushi's pocket is Rs. 1600, then find the sum gifted by anushka.

Answer 1

Let Anushka and Arushi have equal amount of money in their packet, which is Rs. x.
After giving $\frac{1}{3}$ of the money of Anushka to Arushi,
Amount of Arushi=Rs. $(x+\frac{x}{3})$
According to the question,
$(x+\frac{x}{3})-\frac{1}{2}\times (x+\frac{x}{3})=1600\Rightarrow (x+\frac{x}{3})(1-\frac{1}{2})=1600\Rightarrow (x+\frac{x}{3})\times \frac{1}{2}=1600\Rightarrow \frac{3x+3}{3}=1600\times 2\Rightarrow \frac{4x}{3}=3200\therefore x=3200\times \frac{3}{4}=2400$
So, money gifted by Anushka= $\frac{1}{3}$ of 2400=$\frac{1}{3}\times 2400$=Rs. 800