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Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. P invested Rs. 10000 more than Q in a business, but at the end of the year, they received profit in the ratio 11 ∶ 10, such that P received Rs. 2100 more than Q. R and S also invested in another business in the ratio 1 ∶ 2, but at the end of the year, they received profit in the ratio 6∶ 7, such that R received Rs. 2400 less than S. Quantity A: If P withdrew Rs. 10000 after 6 months of investment, how much money did he initially invested? Quantity B: If S withdrew Rs. 50000 after 4 months of investment, how much money did he initially invested? Quantity C: How much total profit did all four of them earned at the end of the year?

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. P invested Rs. 10000 more than Q in a business, but at the end of the year, they received profit in the ratio 11 ∶ 10, such that P received Rs. 2100 more than Q. R and S also invested in another business in the ratio 1 ∶ 2, but at the end of the year, they received profit in the ratio 6∶ 7, such that R received Rs. 2400 less than S. Quantity A: If P withdrew Rs. 10000 after 6 months of investment, how much money did he initially invested? Quantity B: If S withdrew Rs. 50000 after 4 months of investment, how much money did he initially invested? Quantity C: How much total profit did all four of them earned at the end of the year? Correct Answer Quantity A < Quantity B > Quantity C

Solving for Quantity A:

Let Q’s initial investment be Rs. ‘x’

⇒ P’s initial investment = Rs. (x + 10000)

∵ P withdrew Rs. 10000 after 6 months,

⇒ P’s total capital investment = 6(x + 10000) + 6x = 12x + 60000

∵ Ratio of profit = Ratio of capital investment

⇒ 11/10 = (12x + 60000)/12

⇒ 132x = 120x + 600000

⇒ x = 600000/12 = Rs. 50000

⇒ Quantity A = P’s initial investment = 50000 + 10000 = Rs. 60000

Solving for Quantity B:

Let the initial investment of R and S be Rs. ‘y’ and Rs. ‘2y’ respectively

⇒ R’s total capital investment = 12y

∵ S withdrew Rs. 50000 after 4 months,

⇒ S’ total capital investment = (4 × 2y) + 8(2y – 50000) = 24y – 400000

∵ Ratio of profit = Ratio of capital investment

⇒ 6/7 = 12y/(24y – 400000)

⇒ 144y – 2400000 = 84y

⇒ y = 2400000/60 = Rs. 40000

⇒ Quantity B = S’s initial investment = 2y = Rs. 80000

Solving for Quantity C:

Let the profit earned by P and Q be Rs. ‘11u’ and ‘10u’ respectively

⇒ 11u – 10u = Rs. 2100

⇒ u = Rs. 2100

⇒ Total profit earned by P and Q = 11u + 10u = 21u = 21(2100) = Rs. 44100

Let the profit earned by R and S be Rs. ‘6v’ and ‘7v’ respectively

⇒ 7v – 6v = Rs. 2400

⇒ v = Rs. 2400

⇒ Total profit earned by R and S = 6v + 7v = 13v = 13(2400) = Rs. 31200

⇒ Quantity C = Total profit earned by P, Q, R, S = 44100 + 31200 = Rs. 75300

∴ Quantity A < Quantity B > Quantity C

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