Multiple choice

Arjun invested Rs. 2,400 and Bhaskar invested Rs. 3,600 in a startup. After the completion of four successful months of the startup, Keshav also invested Rs. X in this startup. After the completion of eight successful months of the startup, Bhaskar withdrew Rs. 600. When the annual profit was calculated, it came out to be Rs. 22,500 and Keshav's share in this profit was Rs. 8,000. What is the value of X?

  1. Rs. 4,800

  2. Rs. 5,000

  3. Rs. 4,600

  4. Rs. 4,200

  5. Rs. 5,200
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A Correct answer
Explanation

Calculate the investment-months for each: Arjun = 2400 * 12 = 28800. Bhaskar = 3600 * 8 + 3000 * 4 = 28800 + 12000 = 40800. Keshav = X * 8. Total = 69600 + 8X. Keshav's share = (8X / (69600 + 8X)) * 22500 = 8000. Solving for X gives 4800.

AI explanation

Using the partnership profit sharing ratio method, we find the effective capital multiplied by the time period for each person. Arjun's ratio is 2400 * 12 = 28800, Bhaskar's ratio is (3600 * 8) + (3000 * 4) = 40800, and Keshav's ratio is X * 8. Keshav's share of 8000 out of the total 22500 gives the equation 8000 / 22500 = 8X / (28800 + 40800 + 8X), which simplifies to 32 / 90 = X / (8700 + X). Solving this yields 32(8700 + X) = 90X, meaning 278400 = 58X, so X equals 4800.

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