anushka and arushi are friends.they have equal money in their pockets . anshuka gave 1/3 of her money to arushi as birthday gift. then arushi gave a party at a restaurant and cleared the bill by payng the half of the total money with her. if the remaining money in aarushi's pocket is rupees 1600, find the sum gifted by anushka
Answers
Let, Aarushi and Anushka have the same amount of money in their pocket, which is Rs.x.
After Anushka gives
31rd
of the money to Aarushi-
Amount with Aarushi= (x+ x3 )
As per question-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
⇒(x+ 3x)− 21 ×(x+ 3x )=1600
[Taking (x+
3x ) common]⇒(x+ 3x )(1− 21 )=1600⇒( 33x+x )( 22−1)=1600⇒ 34 × 21 =1600⇒ 64x=1600⇒4x=9600⇒x= 49600 =2400
Therefore, the equal amount of money in Anushka and Aarushi's pocket is Rs.2400.
Money gifted by Anushka-⇒ 31of 2400⇒ 31×2400⇒800
Therefore, Anushka gave Rs.800 to Aarushi.
Answer:
Solution
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Let, Aarushi and Anushka have the same amount of money in their pocket, which is Rs.x.
After Anushka gives
3
1
rd
of the money to Aarushi-
Amount with Aarushi= (x+
3
x
)
As per question-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
⇒(x+
3
x
)−
2
1
×(x+
3
x
)=1600
[Taking (x+
3
x
) common]
⇒(x+
3
x
)(1−
2
1
)=1600
⇒(
3
3x+x
)(
2
2−1
)=1600
⇒
3
4x
×
2
1
=1600
⇒
6
4x
=1600
⇒4x=9600
⇒x=
4
9600
=2400
Therefore, the equal amount of money in Anushka and Aarushi's pocket is Rs.2400.
Money gifted by Anushka-
⇒
3
1
of 2400
⇒
3
1
×2400
⇒800
Therefore, Anushka gave Rs.800 to Aarushi.