# Anushka and Aarushi are friends.

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, then find the sum gifted by Anushka.

Solution:

Let Anushka and Aarushi have equal amount of money in their packet, which is $₹ x$. After giving $\frac{1}{3}$ of the money of Anushka to Aarushi,

Amount of Aarushi $=₹\left(x+\frac{x}{3}\right)$

According to the question,

$\left(x+\frac{x}{3}\right)-\frac{1}{2} \times\left(x+\frac{x}{3}\right)=1600$

$\Rightarrow$ $\left(x+\frac{x}{3}\right)\left(1-\frac{1}{2}\right)=1600$

$\Rightarrow$$\left(x+\frac{x}{3}\right) \times \frac{1}{2}=1600$

$\Rightarrow$ $\frac{3 x+x}{3}=1600 \times 2$

$\Rightarrow$ $\frac{4 x}{3}=3200$

$\therefore$ $x=3200 \times \frac{3}{4}=2400$

So, money gifted by Anushka $=\frac{1}{3}$ of $2400=\frac{1}{3} \times 2400=₹ 800$