A and B invest ₹5,000 and ₹7,000 respectively for one year. If the total profit is ₹3,600, what is B's share?

₹2,100. Profit is split in the ratio of the capitals, 5000 : 7000 = 5 : 7. B's share is 712 3600 = ₹2,100.

A starts a business with ₹20,000. After 4 months B joins with ₹30,000. At the end of the year the profit is ₹9,600. What is B's share?

₹4,800. A's capital-months = 20000 12 = 240000; B's = 30000 8 = 240000. The ratio is 1 : 1, so B gets half of ₹9,600 = ₹4,800.

A, B and C invest in the ratio 2 : 3 : 5 for the same period. If C's profit share is ₹4,500 more than A's, what is the total profit?

₹15,000. The shares are in the ratio 2 : 3 : 5. C's share minus A's is 5 - 2 = 3 parts = ₹4,500, so one part is ₹1,500 and the total (10 parts) is ₹15,000.

In a partnership A takes 25% of the profit for managing and the rest is shared by capital. A and B put in ₹15,000 and ₹25,000. If the total profit is ₹8,000, what is A's total share?

₹4,250. A's management fee is 25\% of ₹8,000 = ₹2,000. The remaining ₹6,000 is split 15000 : 25000 = 3 : 5, so A's capital share is 38 6000 = ₹2,250. A's total is 2000 + 2250 = ₹4,250.

A and B start with ₹3,000 and ₹4,000. After 8 months A adds ₹2,000 more. At the end of the year the profit is ₹6,900. What is B's share?

₹3,600. A's capital-months = 3000 8 + 5000 4 = 44,000; B's = 4000 12 = 48,000. The ratio is 11 : 12 (total 23), so B's share is 1223 6900 = ₹3,600.

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Partnership — Questions & Answers

In a partnership, profit is divided in the ratio of each partner's capital multiplied by the time it stayed in the business. A working partner may also draw a fixed amount before the split.

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Key formulas

Profit share ratio $= C_1 t_1 : C_2 t_2 : C_3 t_3$ (capital $\times$ months)
If capitals are equal, split by time; if times are equal, split by capital
Remove any fixed salary or commission from total profit before applying the ratio

5 solved Partnership questions

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01
A and B invest ₹5,000 and ₹7,000 respectively for one year. If the total profit is ₹3,600, what is B's share?
5 steps · reveal one at a time
1. Step 1: Identify Investments
  A and B invested \u20b95,000 and \u20b97,000 respectively. The total profit to be shared after one year is \u20b93,600. We need to find B's share of this profit.
2. Step 2: Calculate Investment Ratio
  Profits are shared in the ratio of the investments. A's investment is \u20b95,000 and B's is \u20b97,000. So, the ratio of their investments is $5000 : 7000$ , which simplifies to $5 : 7$ .
3. Step 3: Find B's Profit Fraction
  The total parts in the ratio are $5 + 7 = 12$ . B's share corresponds to 7 parts out of these 12. Therefore, B's fraction of the total profit is $\frac{7}{12}$ .
4. Step 4: Calculate B's Share
  To find B's share, multiply B's fraction of the profit by the total profit. B's share is $\frac{7}{12} \times \u20b93,600 = \u20b92,100$ .
5. Step 5: The answer
  So the answer is (D) \u20b92,100. This is calculated by finding B's proportional share based on their investment ratio.
02
A starts a business with ₹20,000. After 4 months B joins with ₹30,000. At the end of the year the profit is ₹9,600. What is B's share?
4 steps · reveal one at a time
1. Step 1: A's total investment
  A invested ₹20,000 for the entire year (12 months). So, A's total capital-months is $20000 \times 12 = 240000$ . This represents A's contribution over time.
2. Step 2: B's total investment
  B joined after 4 months, meaning B invested for $12 - 4 = 8$ months. B's capital was ₹30,000. So, B's total capital-months is $30000 \times 8 = 240000$ .
3. Step 3: Determine profit ratio
  Profits are shared in proportion to the capital-months. The ratio of A's capital-months to B's capital-months is $240000 : 240000$ , which simplifies to $1 : 1$ .
4. Step 4: The answer
  So the answer is (B) ₹4,800. Since the profit sharing ratio is $1:1$ , B gets half of the total profit. Half of ₹9,600 is ₹4,800.
03
A, B and C invest in the ratio 2 : 3 : 5 for the same period. If C's profit share is ₹4,500 more than A's, what is the total profit?
4 steps · reveal one at a time
1. Step 1: Understand the Ratios
  A, B, and C invest in the ratio $2 : 3 : 5$ . This means their profit shares will also be in the same ratio. We can think of these as "parts" of the total profit.
2. Step 2: Find Difference in Shares
  We're told C's profit share is \u20b94,500 more than A's. In terms of ratio parts, C has $5$ parts and A has $2$ parts. The difference is $5 - 2 = 3$ parts.
3. Step 3: Calculate One Part's Value
  Since the difference of $3$ parts is equal to \u20b94,500, we can find the value of one part. One part is equal to $\u20b94,500 \div 3 = \u20b91,500$ .
4. Step 4: The answer
  So the answer is (B) \u20b915,000. The total profit is the sum of all parts: $2 + 3 + 5 = 10$ parts. Therefore, the total profit is $10 \times \u20b91,500 = \u20b915,000$ .
04
In a partnership A takes 25% of the profit for managing and the rest is shared by capital. A and B put in ₹15,000 and ₹25,000. If the total profit is ₹8,000, what is A's total share?
4 steps · reveal one at a time
1. Step 1: Calculate A's Fee
  First, calculate A's management fee. This is $25\%$ of the total profit. So, $25\% \times \text{\text{Rs}\,}8,000 = \text{\text{Rs}\,}2,000$ . This is the first part of A's total share.
2. Step 2: Profit for Capital
  Next, find the remaining profit to be shared based on capital. Subtract A's management fee from the total profit: $\text{\text{Rs}\,}8,000 - \text{\text{Rs}\,}2,000 = \text{\text{Rs}\,}6,000$ . This amount will be distributed.
3. Step 3: A's Capital Share
  A and B's capital ratio is $\text{\text{Rs}\,}15,000 : \text{\text{Rs}\,}25,000$ , which simplifies to $3 : 5$ . A's share of the remaining profit is $\frac{3}{3+5} \times \text{\text{Rs}\,}6,000 = \frac{3}{8} \times \text{\text{Rs}\,}6,000 = \text{\text{Rs}\,}2,250$ .
4. Step 4: The answer
  So the answer is (C) ₹4,250. A's total share is the sum of the management fee and the capital share: $\text{\text{Rs}\,}2,000 + \text{\text{Rs}\,}2,250 = \text{\text{Rs}\,}4,250$ .
05
A and B start with ₹3,000 and ₹4,000. After 8 months A adds ₹2,000 more. At the end of the year the profit is ₹6,900. What is B's share?
4 steps · reveal one at a time
1. Step 1: A's Total Investment
  A starts with $\text{Rs}\,3,000$ for $8$ months. After adding $\text{Rs}\,2,000$ , A's investment becomes $\text{Rs}\,5,000$ for the remaining $4$ months. So, A's total capital-months is $3000 \times 8 + 5000 \times 4 = 44000$ .
2. Step 2: B's Total Investment
  B invests $\text{Rs}\,4,000$ for the entire year, which is $12$ months. Therefore, B's total capital-months is $4000 \times 12 = 48000$ .
3. Step 3: Find Investment Ratio
  The ratio of A's capital-months to B's capital-months is $44000 : 48000$ . Simplifying this ratio by dividing both by $4000$ gives us $11 : 12$ . The total ratio parts are $11 + 12 = 23$ .
4. Step 4: The answer
  So the answer is (C) ₹3,600. B's share of the profit is calculated based on their investment ratio. B's share is $\frac{12}{23}$ of the total profit, so $\frac{12}{23} \times 6900 = \text{Rs}\,3,600$ .

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