Question:hard

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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Add up each partner's capital for every one of the 13 months to get their capital-month totals, then split the profit in that ratio.
Updated On: Jul 21, 2026
  • Rs. 22,000
  • Rs. 33,000
  • Rs. 42,000
  • Rs. 46,000
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The Correct Option is C

Solution and Explanation

Step 1: Use the average capital shortcut instead of adding 13 terms.
Since M's capital drops by a fixed Rs. 1000 every month, it forms an arithmetic sequence, and the average of an arithmetic sequence equals the average of its first and last terms.

Step 2: Find M's first and last month capital.
Month 1: \(35000-1000=34000\). Month 13: \(35000-13000=22000\).
\[ \text{Average capital of M} = \frac{34000+22000}{2} = 28000 \]
Capital-month total for M \(= 28000\times13 = 364000\), matching the direct sum.

Step 3: Do the same for N.
Month 1: \(22000+1000=23000\). Month 13: \(22000+13000=35000\). \[ \text{Average capital of N} = \frac{23000+35000}{2} = 29000 \] Capital-month total for N \(=29000\times13=377000\).

Step 4: Form the ratio and split the profit. \[ M:N = 364000:377000 = 28:29 \] Each of the 57 parts is worth \(85500/57=1500\), so M gets \(28\times1500=42000\).
The average-capital shortcut avoids adding up 13 separate months and gives the same share. \[ \boxed{Rs.\ 42{,}000} \]
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