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A, B and C entered into a partnership business, A invested Rs. x, B invested 20% more than A and C invested \(111\frac{1}{9}\% \) of B. After 8 months B left the business and A withdraws 50% of his investment and after 2 more months A left the business whereas C increased his investment by 12.5%. Quantity I: If at the end of the year difference between profit shares of C and (A + B) together is Rs. 2822, then find the profit share of C? Quantity II: If total profit is Rs. 198596, then find the average of the profit share of (A + B) together?

A, B and C entered into a partnership business, A invested Rs. x, B invested 20% more than A and C invested \(111\frac{1}{9}\% \) of B. After 8 months B left the business and A withdraws 50% of his investment and after 2 more months A left the business whereas C increased his investment by 12.5%. Quantity I: If at the end of the year difference between profit shares of C and (A + B) together is Rs. 2822, then find the profit share of C? Quantity II: If total profit is Rs. 198596, then find the average of the profit share of (A + B) together? Correct Answer Quantity I < Quantity II

Quantity I:

Ratio of investment of A, B and C

⇒ x : 6x / 5 : 4x / 3

⇒ 15x : 18x : 20x

Quantity I:

Profit share of A : B : C = (15x × 8 + 7.5x × 2) : (18x × 8) : (20x × 10 + 22.5 × 2)

⇒ 135x : 144x : 245x

Now,

(A + B) - C = 2822

⇒ 279x - 245x = 2822

⇒ x = 83

∴ Profit share of C = 245 × 83 = Rs. 20335

Quantity II:

Profit share of A = 135 / 524 × 198596 = 135 × 379 = 51165

Profit share of B = 144 / 524 × 198596 = 144 × 379 = 54576

Average profit of A and B = (51165 + 54576) / 2 = Rs. 52870.5

∴ Quantity I < Quantity II

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