Multiple choice

A, B and C enter into a partnership by investing in the ratio of 3: 2: 4. After one year, B invests another Rs. 2,70,000 and C at the end of 2 years, also invests Rs. 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4: 5. Find the initial investment of C.

  1. Rs. 2,70,000

  2. Rs. 1,80,000

  3. Rs. 3,60,000

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial investments be 3x, 2x, 4x. A's contribution: 3x * 3 years = 9x. B's contribution: 2x * 1 year + (2x + 270000) * 2 years = 6x + 540000. C's contribution: 4x * 2 years + (4x + 270000) * 1 year = 12x + 270000. Ratio of profits 3:4:5. Solve 9x / (6x + 540000) = 3/4 to find x = 360000 / 4 = 90000. C's initial = 4x = 360000.

AI explanation

Let the initial investments of A, B, and C be 3x, 2x, and 4x respectively. Over 3 years, the ratio of their profit shares is calculated as (3x x 3) : (2x x 1 + (2x + 270000) x 2) : (4x x 2 + (4x + 270000) x 1), which equals 3 : 4 : 5. Simplifying the products gives the ratio 9x : (6x + 540000) : (12x + 270000). By equating A and B to the given ratio, we have 9x / (6x + 540000) = 3 / 4, which yields 36x = 18x + 1620000, meaning 18x = 1620000 and x = 90000. C's initial investment is 4x, which equals 4 x 90000 = Rs. 3,60,000.

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