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Question
Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?
Solution
Let x be the proportionality constant.
Since, capitals invested by Mr. Natarajan and Mr. Gopalan are in the ratio 4:5
∴ their capitals are Rs 4x and Rs 5x respectively
Let Natarajan’s period of investment in the company be y months
∴ Natarajan invested Rs 4x for y months and Gopalan invested Rs 5x for 16 months
Since, capitals and period of investment both are different.
∴ profit is distributed in the ratio of the product of the capitals and respective period.
i.e., in the ratio `(4x xx y):(5x xx 16)`
i.e., in the ratio 4xy : 80x
i.e., in the ratio y : 20
But, given profit is in the ratio 5:4.
`:.y/20=5/4`
`:.y =5/4xx20`
∴ y = 25
∴ Mr. Natarajan’s investment in the company was for 25 months.
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