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Anushka and Aarushi are friends. They have an 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:

Given, Anushka and Aarushi have an equal amount of money in their pockets.

Anushka gave 1/3 of her money to Aarushi as her birthday gift.

Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her.

Remaining money in Aarushi’s pocket is Rs.1600

We have to find the sum gifted by Anushka.

Let the initial amount of Anushka and Aarushi be Rs. x

After Anushka gives 1/3 of her money to Aarushi,

Amount of Aarushi = (x + x/3)

Restaurant bill paid by Aarushi = 1/2 (x + x/3)

Remaining money = (x + x/3) - 1/2 (x + x/3)

= 1/2 (x + x/3)

According to the question,

1/2 (x + x/3) = 1600

x + x/3 = 1600(2)

4x/3 = 3200

4x = 3200(3)

4x = 9600

x = 9600/4

x = 2400

Initial amount of Anushka and Aarushi is Rs. 2400.

Now, x/3 = 2400/3

= 800

Therefore, the sum gifted by Anushka is Rs. 800.

✦ Try This: Ram and Sam are friends. They have an equal amount of money in their pockets. Ram gave ¼ of his money to Sam as his birthday gift. Then Sam gave a party at a restaurant and cleared the bill by paying half of the total money with him. If the remaining money in Sam’s pocket is Rs.2300, find the sum gifted by Ram.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 2

NCERT Exemplar Class 8 Maths Chapter 4 Problem 82

Anushka and Aarushi are friends. They have an 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

Summary:

Anushka and Aarushi are friends. They have an 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, the sum gifted by Anushka is Rs. 800

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