Multiple choice

A and B started a partnership business by investing some amount in the ratio of 5 : 6. C joined after 6 months with an amount equal to 2/3rd of B's share. What was their profit (in Rs.) at the end of the year if C got Rs. 21,600 as his share?

  1. 46,800

  2. 56,160

  3. 70,200

  4. 1,40,400
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the investments be 5x and 6x. C invests 2/3 of 6x, which is 4x. A and B invest for 12 months, C for 6 months. Ratio of profit shares = (5x*12) : (6x*12) : (4x*6) = 60 : 72 : 24 = 5 : 6 : 2. Given 2 parts = 21,600, so 1 part = 10,800. Total profit = (5+6+2) * 10,800 = 13 * 10,800 = 140,400.

AI explanation

Assuming the investments of A and B are 5x and 6x, C's investment is 2/3 of B's investment, which equals 4x. The ratio of their profit shares is the product of investment and time: A's share is 5x for 12 months (60x), B's share is 6x for 12 months (72x), and C's share is 4x for 6 months (24x). The profit ratio is 60 : 72 : 24, which simplifies to 5 : 6 : 2, making the total 13 parts. If C's 2 parts equal 21600, then the total profit of 13 parts is (21600 / 2) * 13, which equals 140400.

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