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Question
John and Mathew started a business with their capitals in the ratio 8 : 5. After 8 months, john added 25% of his earlier capital as further investment. At the same time, Mathew withdrew 20% of bis earlier capital. At the end of the year, they earned ₹ 52000 as profit. How should they divide the profit between them?
Solution
John's and Mathew's capitals are in the ratoo 8 : 5 .
∴ Their capitals are 8x and 5x respectively for 8 months
25% of John's capital = `25/100 xx 8x = 2x`
John added 2x in his earlier capital.
∴ 8x+ 2x = 10x is capital for next 4 months.
20% of the capital of Mathew = `20/100 xx 5x = x`
Mathew Withdrew x from his earlier capital.
∴ 5x - x = 4x is capital for next 4 months.
Profit distributed in the ratio
(8x x 8 + 10x x 4) : (5x x 8 + 4x x 4)
(64x + 40x) : (40x + 16x)
104x : 56x
13 : 7
John's profit = `13/20 xx 52000 = ₹ 33,800`
Mathew's profit = `7/20 xx 52000 = ₹ 18,200`
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