Question

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 N?

• A. Rs. 22,500
• B. Rs. 33,000
• C. Rs. 43,500
• D. Rs. 46,000

Hint:

Use capital multiplied by number of months for each partner to find the profit-sharing ratio.

Answer 1

The Correct Option is C

Step 1: Track M's capital month by month. M starts with Rs. 35,000 and withdraws Rs. 1000 every month, so over the 13 months M's monthly capital runs from Rs. 34,000 in month 1 down to Rs. 22,000 in month 13, falling by Rs. 1000 each month.
Step 2: Track N's capital month by month. N starts with Rs. 22,000 and adds Rs. 1000 every month, so N's monthly capital runs from Rs. 23,000 in month 1 up to Rs. 35,000 in month 13, rising by Rs. 1000 each month.
Step 3: Find M's total capital-months. This is an arithmetic series of 13 terms from 34,000 to 22,000, so the sum is \(13 \times \dfrac{34000+22000}{2} = 13 \times 28000 = 364000\).
Step 4: Find N's total capital-months. Similarly, the sum is \(13 \times \dfrac{23000+35000}{2} = 13 \times 29000 = 377000\).
Step 5: Form the profit-sharing ratio. M : N = 364000 : 377000. Dividing both by 13000 gives 28 : 29.
Step 6: Divide the profit. Total parts = 28 + 29 = 57. N's share = \(\dfrac{29}{57} \times 85500\). Since \(85500/57 = 1500\), N's share = \(1500 \times 29 = 43500\).\[\boxed{\text{Rs. }43{,}500}\]