Question:medium

M and N start a business with respective capitals of Rs. 35,000 and Rs. 22,000. M withdrew an amount of Rs. 1000 every month from the business while N put in an additional amount of Rs. 1,000 every month into the business. If they close the business after 13 months after making a profit of Rs. 85,500, then what is the share of M?

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Work out each partner's total capital-months over the 13 months, then split the profit in that ratio.
Updated On: Jul 20, 2026
  • Rs. 22,000
  • Rs. 33,000
  • Rs. 42,000
  • Rs. 46,000
  • Rs. 48,000
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The Correct Option is C

Solution and Explanation

A quicker way to reach the same capital-months is to use the average monthly capital of each partner. M's capital drops by Rs. 1,000 in steps from month 1 to month 13, so his withdrawals over the period average to $(1000 + 13000)/2 = 7000$. So M's average capital works out to $35000 - 7000 = 28000$, and over 13 months that is $28000 \times 13 = 364000$ capital-months.
N's deposits average the same $7000$, so his average capital is $22000 + 7000 = 29000$, giving $29000 \times 13 = 377000$ capital-months.
The ratio is $364000 : 377000 = 28 : 29$, so out of the total profit of Rs. 85,500 split into 57 parts, M gets $85500 \times 28/57 = 42000$.
M's share is Rs. 42,000.
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