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 the money in each of their pockets initially be 3x
So money given by Anushka to Arushi as her birthday gift = 3x(1/3) = x
Money with Arushi after this gift = 3x + x = 4x
Money Arushi spent on her birthday party = 1/2 of money she had = 1/2 of 4x = 2x

Money remaining with Arushi now = 4x - 2x = 2x
2x = 1600
x = 800
So, money gifted by Anushka = x = 800 rs

Answer 2

Solution:-

given by:-
let Anushka have money = x rupees.
accordung to question:-
anushka gave money for arushi :- 1/3×x = x/3
now Amount of arushi =
$(x + \frac{x}{3} )$
when arushi paid party bill:-
according to quetion:-
$(x + \frac{x}{3} ) - \frac{1}{2} \times (x + \frac{x}{3} ) = 1600 \\ x + \frac{x}{3} - \frac{x}{2} - \frac{x}{6} = 1600 \\ \frac{6x + 2x - 3x - x}{6} = 1600 \\ 4x = 9600 \\ x = 2400$
so money gifted by Anushka :-
$\frac{2400}{3} \\\\ 800rs$

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