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P and Q started a business in partnership by investing in the ratio 3 ∶ 2. But after 8 months of investing, P withdrew Rs. 30000. If at the end of the year, they received profit in the ratio 5 ∶ 4, how much money did Q invest in the business?

P and Q started a business in partnership by investing in the ratio 3 ∶ 2. But after 8 months of investing, P withdrew Rs. 30000. If at the end of the year, they received profit in the ratio 5 ∶ 4, how much money did Q invest in the business? Correct Answer Rs. 40000

Let P and Q started by investing Rs. ‘3x’ and Rs. ‘2x’ respectively

∵ P withdrew Rs. 30000 after 8 months,

⇒ P’s total capital investment = (8 × 3x) + 4 × (3x – 30000) = 24x + 12x – 120000 = 36x – 120000

⇒ Q’s total capital investment = 12 × 2x = 24x

Now,

Ratio of profit shares = Ratio of total capital investments

⇒ 5 ∶ 4 = (36x – 120000) ∶ 24x

⇒ 5 × 24x = 4 × (36x - 120000)

⇒ 120x = 144x - 480000

⇒ 24x = 480000

⇒ 2x = 40000

∴ Q invested Rs. 40000 in the business

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