Multiple choice

Both C and D enter into a business partnership with their initial investments in the ratio of 3 : 4. After 6 months, C withdraws a quarter of his capital, while D increases his capital by 50%. At the end of the year, the business earns a profit of Rs. 9 lakh. What is the share (in Rs. lakhs) of D in the annual profit?

  1. 4.9

  2. 5.9

  3. 7.3

  4. 8.7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial investment ratio C:D = 3:4. Let investments be 3x and 4x. C: (3x * 6) + (3x * 0.75 * 6) = 18x + 13.5x = 31.5x. D: (4x * 6) + (4x * 1.5 * 6) = 24x + 36x = 60x. Ratio C:D = 31.5:60 = 315:600 = 21:40. Total parts = 61. D's share = (40/61) * 9 lakh = 5.9016 lakh.

AI explanation

Using the partnership formula, the profit share is proportional to the product of investment and time. Assuming initial investments of 3x and 4x, C's effective capital for the year is (3x for 6 months) plus (2.25x for 6 months), totaling 31.5x, while D's effective capital is (4x for 6 months) plus (6x for 6 months), totaling 60x. The profit ratio of C to D is 31.5 to 60, which equals 21 to 40, meaning there are 61 total parts for the 9 lakh profit. D's share is 40 parts of the profit, so D receives (40 divided by 61) multiplied by 9 lakhs, which is approximately 5.9 lakhs.

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