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The ratio of the incomes of Chetan and Dinesh is 3 : 4. The ratio of their expenditures is 5 : 7. If each of them saves Rs. 200, find the incomes of both ?
The ratio of the incomes of Chetan and Dinesh is 3 : 4. The ratio of their expenditures is 5 : 7. If each of them saves Rs. 200, find the incomes of both ?
A). Rs. 1500, Rs. 2000
B). Rs. 600, Rs. 800
C). Rs. 900, Rs. 1200
D). Rs. 1800, Rs.2400
This Question has 2 answers.
$ \text{Let the incomes of Chetan and Dinesh be } 3x \text{ and } 4x \text{ respectively.} $
$ \text{Let the expenditures of Chetan and Dinesh be } 5y \text{ and } 7y \text{ respectively.} $
$ \text{According to the given condition:} $
$ 3x - 5y = 200 $
$ 4x - 7y = 200 $
$ \text{Solving for } x \text{ and } y: $
$ \text{Multiplying the first equation by 4:} $
$ 12x - 20y = 800 $
$ \text{Multiplying the second equation by 3:} $
$ 12x - 21y = 600 $
$ \text{Subtracting:} $
$ (12x - 20y) - (12x - 21y) = 800 - 600 $
$ y = 200 $
$ \text{Substituting } y = 200 \text{ in } 3x - 5y = 200: $
$ 3x - 5(200) = 200 $
$ 3x - 1000 = 200 $
$ 3x = 1200 $
$ x = 400 $
$ \text{Incomes:} $
$ 3x = 3(400) = 1200 $
$ 4x = 4(400) = 1600 $
Thanks
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