Multiple choice

A, B, C, D and E start a partnership firm. Capital contributed by A is three times that contributed by D. E contributes half of A's contribution, B contributes one-third of E's contribution and C contributes two-third of A's contribution. If the difference between the combined shares of A, D and E and the combined shares of B and C in the total profit of the firm is Rs. 13,500, what is the combined share of B, C and E? (The shares are supposed to be proportional to the contributions)

  1. Rs. 13,500

  2. Rs. 18,000

  3. Rs. 19,750

  4. Rs. 20,250
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let D = x. Then A = 3x, E = 1.5x, B = 0.5x, C = 2x. Total = 3x + x + 1.5x + 0.5x + 2x = 8x. Combined (A,D,E) = 3x + x + 1.5x = 5.5x. Combined (B,C) = 0.5x + 2x = 2.5x. Difference = 3x = 13500, so x = 4500. Combined (B,C,E) = 0.5x + 2x + 1.5x = 4x = 4 * 4500 = 18000.

AI explanation

Let D's capital be 1 unit, making A's capital 3, E's capital 1.5, B's capital 0.5, and C's capital 2. The combined ratio of shares for A, D, and E is 5.5, while the combined ratio for B and C is 2.5, making the total ratio 8. The difference between the combined shares is 3 ratio units, which equals Rs. 13,500, meaning 1 ratio unit is Rs. 4,500. The combined share of B, C, and E is 4 ratio units (2.5 plus 1.5), which totals Rs. 18,000.

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