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Q.

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, then the sum gifted by Anushka is Rs. ____.


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Detailed Solution

Anushka and Aarushi are friends. They have an equal amount of money in their pockets. Anushka gave Question Image 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 the sum gifted by Anushka is Rs. 800.
Assuming Aarushi and Anushka have the equal sum of cash in their take, that is Rs. x.
According to given condition:
Anushka gives ( 1 3 ) rd   of the cash to Aarushi.
So, Aarushi has amount =(x+ x 3 )   .
Aarushi gave a party and cleared the bill by paying half of the whole cash with her.
Also, remaining money in Aarushi's pocket is Rs. 1600.
  (x+ x 3 ) 1 2 ×(x+ x 3 )=1600   (x+ x 3 )(1 1 2 )=1600  
3x+x 3 21 2 =1600 4x 3 × 1 2 =1600 4x 6 =1600 4x=9600 x= 9600 4 x=2400   Now, amount of birthday gift:
1 3 ×2400 800  
Therefore, the sum gifted by Anushka is Rs. 800 to Ayushi.
 
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