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P, Q, and R invested in a business in partnership in the ratio 5 ∶ 2 ∶ 8. After 3 months, P withdrew 60% of his investment, while Q increased his investment by 50%. After 4 more months, Q withdrew 20% of his investment, while R increased his investment by 30%. At the end of the year, if R received Rs. 5200 more than Q as his profit share at the end of the year, then how much profit will P receive at the end of the year? 

P, Q, and R invested in a business in partnership in the ratio 5 ∶ 2 ∶ 8. After 3 months, P withdrew 60% of his investment, while Q increased his investment by 50%. After 4 more months, Q withdrew 20% of his investment, while R increased his investment by 30%. At the end of the year, if R received Rs. 5200 more than Q as his profit share at the end of the year, then how much profit will P receive at the end of the year?  Correct Answer Rs. 2200

Let the initial investments of P, Q and R be ‘5x’, ‘2x’ and ‘8x’ respectively 

P withdrew 60% of his investment after 3 months 

⇒ P’s actual investment = (5x × 3) + (0.4 × 5x × 9) = 15x + 18x = 33x

Q increased his investment by 50% after 3 months & withdrew 20% of his investment after 4 more months 

⇒ Q’s actual investment = (2x × 3) + (1.5 × 2x × 4) + (0.8 × 1.5 × 2x × 5) = 6x + 12x + 12x = 30x

R increased his investment by 30% after 3 + 4 = 7 months 

⇒ R’s actual investment = (8x × 7) + (1.3 × 8x × 5) = 56x + 52x = 108x

∵ Ratio of profit shares = Ratio of actual investments 

⇒ Ratio of profit shares of P, Q & R = 33x ∶ 30x ∶ 108x = 11 ∶ 10 ∶ 36 

Sum of ratios = 11 + 10 + 36 = 57

Given, R received Rs. 5200 more than Q as his profit share,

⇒ × Total profit = 5200

⇒ Total profit = 57/26 × 5200 = Rs. 11400

∴ Profit earned by P = (11/57) × 11400 = Rs. 2200

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