X, Y and Z started a business with investment of Rs. (a-1200), Rs. (a) & Rs.…

2022

X, Y and Z started a business with investment of Rs. (a-1200), Rs. (a) & Rs. (a+1800) respectively. Profit of Y is invested in a scheme which offers simple interest at the rate of 18% p.a. for five years and interest received is Rs.3600. If the total profit in the business is Rs.4800 more than the double of the profit of Y, then which of the following statement/s is/are correct.
(A) value of ‘a’ is multiple of 12.
(B) Z gets 37.5% of the total profit.
(C) Sum of the investment of X & Y is completely divisible of by 8.

  1. A.

    None of these

  2. B.

    Only (C)

  3. C.

    Both (C) & (B)

  4. D.

    Only (B)

  5. E.

    Both (A) & (C)

Attempted by 1 students.

Show answer & explanation

Correct answer: E

Concept

In a partnership where all partners invest for the same duration, profit is divided in the ratio of the capitals invested. Simple Interest is SI = (P × R × T) / 100, so the principal can be recovered as P = (SI × 100) / (R × T). Each partner's share of profit = Total Profit × (that partner's capital ÷ total capital).

Application

  1. Y's profit was invested at SI. Given SI = 3600, R = 18% and T = 5 years: Y's profit = (3600 × 100) / (18 × 5) = 360000 / 90 = Rs. 4000.

  2. Total profit = 4800 more than double of Y's profit = 4800 + 2 × 4000 = Rs. 12800.

  3. Capitals are (a−1200), a and (a+1800); total capital = 3a + 600. Y's share of total profit equals Y's profit: 12800 × a / (3a + 600) = 4000.

  4. Solve: 12800a = 4000(3a + 600) = 12000a + 2400000, so 800a = 2400000, giving a = 3000.

  5. Capitals become X = 1800, Y = 3000, Z = 4800; total = 9600. Shares = 12800 × (capital/9600): X = 2400, Y = 4000, Z = 6400.

Checking each statement

  • (A) a = 3000 = 12 × 250, so a is a multiple of 12 — TRUE.

  • (B) Z's share = 6400 out of 12800 = 50%, not 37.5% — FALSE.

  • (C) Investment of X and Y = 1800 + 3000 = 4800 = 8 × 600, divisible by 8 — TRUE.

Cross-check

Shares 2400 : 4000 : 6400 reduce to 3 : 5 : 8, matching capitals 1800 : 3000 : 4800, and they sum to 12800 — consistent. So statements (A) and (C) are correct while (B) is not.

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