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Question
Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.
Solution
Pocket money of Samidha = Rs. x
Pocket money of Sherya = Rs. y
According to given information, we have
x - 500 = y ....(i)
⇒ x - y = 500
And, y - 500 = `(3)/(5)`x
⇒ 5y - 2500 = 3x
⇒ 5(x - 500) - 2500 = 3x
⇒ 5x - 2500 - 2500 = 3x
⇒ 2x = 5000
⇒ x = 2500
⇒ y
= 2500 - 500
= 2000
THus, pocket money of Samidha is Rs.2500 and that of Sherya is Rs.2000.
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