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प्रश्न
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.
उत्तर
Let the incomes of the two persons be x and y.
`x/y` = `9/7`
⇒ 7x = 9y
⇒ 7x − 9y = 0 ...(I)
Savings of the two persons = Rs 200
Expenses = Income − Savings
`(x − 200)/(y − 200) = 4/3`
∴ 3(x − 200) = 4(y − 200)
⇒ 3x − 600 = 4y − 800
⇒ 3x − 4y = −200 ...(II)
Multiply (I) with 3 and (II) with 7.
21x − 27y = 0 ...(III)
21x − 28y = −1400 ...(IV)
(IV) − (III)
21x − 28y = −1400
21x − 27y = 0
− + −
−y = −1400
⇒ y = 1400
Putting the value y = 1400 in (I) we get
∴ 7x − 9y = 0
∴ 7x − 9(1400) = 0
∴ 7x − 12600 = 0
∴ 7x = 12600
∴ x = `12600/7`
⇒ x = 1800
Thus, the income of the two persons is Rs 1800 and Rs 1400.
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