Q7 of 25 Page 91

The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

As the ratio of incomes is 9 : 7,


Let income of first person = 9x


Income of second person = 7x


Also, ratio of incomes is 4 : 3,


Let expenses of first person = 4y


Expenses of second person = 3y


Each person saves 200 Rs,


⇒ 9x - 4y = 200 eq.[1]


⇒ 7x - 3y = 200 eq.[2]


Multiplying eq.[1] by 3 both side and Multiplying eq.[2] by 4 both side, we get


⇒ 27x - 12y = 600 eq.[3]


⇒ 28x - 12y = 800 eq.[4]


Subtracting eq.[3] from eq.[4], we get


⇒ 28x - 12y - (27x - 12y) = 800 - 600


⇒ 28x - 12y - 27x + 12y = 200


⇒ x = 200


Income of first person = 9x = 9(200) = 1800 Rs


Income of second person = 7x = 7(200) = 1400 Rs


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