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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. X, Y and Z invested Rs. 2 lakhs, Rs. 2.5 lakhs and Rs. 3.5 lakhs in a business respectively. After 4 months, X again invested Rs. 1 lakh, while Z withdrew Rs. 50000. After 2 more months, Y invested Rs. 50000 more, while Z again withdrew Rs. 50000. After another 4 months, X and Y also withdrew Rs. 1 lakh and Rs. 1.5 lakhs respectively. Quantity A: What part of the profit will X receive at the end of the year? Quantity B: What part of the profit will Y receive at the end of the year? Quantity C: What part of the profit will Z receive 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. X, Y and Z invested Rs. 2 lakhs, Rs. 2.5 lakhs and Rs. 3.5 lakhs in a business respectively. After 4 months, X again invested Rs. 1 lakh, while Z withdrew Rs. 50000. After 2 more months, Y invested Rs. 50000 more, while Z again withdrew Rs. 50000. After another 4 months, X and Y also withdrew Rs. 1 lakh and Rs. 1.5 lakhs respectively. Quantity A: What part of the profit will X receive at the end of the year? Quantity B: What part of the profit will Y receive at the end of the year? Quantity C: What part of the profit will Z receive at the end of the year? Correct Answer (Quantity A = Quantity B) < Quantity C

X initially invested Rs. 2 lakhs, again invested Rs. 1 lakh after 4 months, but withdrew Rs. 1 lakh after another 6 months

⇒ X’s total capital investment = (4 × 2) + (6 × 3) + (2 × 2) = 8 + 18 + 4 = Rs. 30 lakhs

Y initially invested Rs. 2.5 lakhs, again invested Rs. 0.5 lakh after 6 months, but withdrew Rs. 1.5 lakh after another 4 months

⇒ Y’s total capital investment = (6 × 2.5) + (4 × 3) + (2 × 1.5) = 15 + 12 + 3 = Rs. 30 lakhs

Z initially invested Rs. 3.5 lakhs, withdrew Rs. 0.5 lakh after 4 months, and again withdrew Rs. 0.5 lakh after another 2 months

⇒ Z’s total capital investment = (4 × 3.5) + (2 × 3) + (6 × 2.5) = 14 + 6 + 15 = Rs. 35 lakhs

∵ Ratio of profits = Ratio of total capital investments

⇒ Ratio of profits = 30∶ 30∶ 35 = 6∶ 6∶ 7

Sum of ratios = 6 + 6 + 7 = 19

Solving for Quantity A:

⇒ Quantity A = Part of profit X received = 6/19

Solving for Quantity B:

⇒ Quantity B = Part of profit Y received = 6/19

Solving for Quantity C:

⇒ Quantity C = Part of profit Z received = 7/19

∴ (Quantity A = Quantity B) < Quantity C

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