Multiple choice

$A$ and $B$ started a business with the amount in the ratio of $6 : 3.$ After $6$ months $C$ joins them with the same amount as $A$. If the total profit at the end of a year was $ 14960$. What is the share of $C$?

  1. Rs.$ 3500$
  2. Rs. $3740$
  3. Rs. $4120$

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

A invests 6 units for 12 months, B invests 3 units for 12 months, C invests 6 units for 6 months. Ratio of shares = (6*12) : (3*12) : (6*6) = 72 : 36 : 36 = 2 : 1 : 1. C's share = (1/4) * 14960 = 3740.

AI explanation

The profit ratio equals the product of investment and time, so let the initial ratio units be 6 for A, 3 for B, and C joins with 6 units. The effective capital products are A at 6 * 12 = 72, B at 3 * 12 = 36, and C at 6 * 6 = 36. This creates a profit sharing ratio of 72 : 36 : 36, which simplifies to 2 : 1 : 1, meaning C receives 1 part out of the 4 total parts. C's share of the Rs. 14960 total profit is (1 / 4) * 14960, which is Rs. 3740.

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