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P and Q started a business by investing Rs. 80000 and Rs. 120000 respectively. After 4 months, they withdrew Rs. 40000 and Rs. 50000 respectively, while R invested Rs. 60000 in their business. If R received profit of Rs. 18000 at the end of the year, how much total profit did the business earned?

P and Q started a business by investing Rs. 80000 and Rs. 120000 respectively. After 4 months, they withdrew Rs. 40000 and Rs. 50000 respectively, while R invested Rs. 60000 in their business. If R received profit of Rs. 18000 at the end of the year, how much total profit did the business earned? Correct Answer Rs. 81000

As, P invested Rs. 80000 and withdrew Rs. 40000 after 4 months,

⇒ P’s total capital investment = (4 × 80000) + (8 × 40000) = 320000 + 320000 = Rs. 640000

Also, Q invested Rs. 120000 and withdrew Rs. 50000 after 4 months

⇒ Q’s total capital investment = (4 × 120000) + (8 × 70000) = 480000 + 560000 = Rs. 1040000

Now, R invested Rs. 60000 after 4 months

⇒ R’s total capital investment = 8 × 60000 = Rs. 480000

Now,

⇒ Ratio of their profits = Ratio of their investments

⇒ Ratio of their profits = 640000 ∶ 1040000 ∶ 480000 = 8 ∶ 13 ∶ 6

⇒ Sum of ratios = 8 + 13 + 6 = 27

Now,

⇒ R’s share in profit = (6/27) of Total profit

⇒ 18000 = (6/27) × Total profit

⇒ Total profit = (27/6) × 18000 = Rs. 81000

∴ Total profit earned by the business is Rs. 81000

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