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प्रश्न
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.
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उत्तर
Let Anushka and Aarushi have equal amount of money in their pocket, which is ₹ x.
After giving `1/3` of the money of Anushka to Aarushi,
Amount of Aarushi = `₹ (x + x/3)`
According to the question,
`(x + x/3) - 1/2 xx (x + x/3) = 1600`
⇒ `(x + x/3)(1 - 1/2) = 1600`
⇒ `(x + x/3)xx 1/2 = 1600`
⇒ `(3x + x)/3 = 1600 xx 2`
⇒ `(4x)/3 = 3200`
∴ `x = 3200 xx 3/4 = 2400`
So, money gifted by Anushka = `1/3` of 2400
= `1/3 xx 2400`
= ₹ 800
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