Partnership Quiz: WBPSC Clerkship 2024
A little practice. A step forward.
12 practice questions on partnership sums for WBPSC Clerkship 2024 arithmetic, each with a worked explanation. 📖 Read the detailed topic
A and B start a business with ₹7,000 and ₹9,000 for one year. If the profit is ₹3,200, what is A's share?
The time is equal, so the profit ratio equals the capital ratio $7 : 9$. The sum is 16 and one part is $3200 \div 16 = 200$. A gets $7 \times 200 =$ ₹1,400. B gets ₹1,800, and the two add up to ₹3,200.
- With equal time, the capital ratio is the profit ratio.
- One part = total profit ÷ sum of the ratio.
- Add the shares to check the total.
A invests ₹4,500 for 12 months and B invests ₹6,000 for 9 months. What is the ratio of their profits?
A's product is $4500 \times 12 = 54000$ and B's is $6000 \times 9 = 54000$. They are equal, so the ratio is $1 : 1$. B has more capital but less time, so 2 : 3 or 3 : 4 is wrong.
- The ratio is of capital × months, not capital alone.
- Equal products mean equal shares.
- Using 4500 : 6000 = 3 : 4 is wrong because the times differ.
- Multiply first, then take the ratio.
A, B and C invest ₹12,000, ₹18,000 and ₹30,000 for equal time. If the total profit is ₹9,000, what is C's share?
The ratio is $12 : 18 : 30 = 2 : 3 : 5$ with sum 10. One part is $9000 \div 10 = 900$. C gets $5 \times 900 =$ ₹4,500. A gets ₹1,800 and B ₹2,700, which add up to ₹9,000.
- Divide by 6000 to simplify the ratio.
- C's part is $ rac{5}{10}$ of the ratio, which is half.
- C's capital is half of the total, so is C's profit.
A starts a business with ₹15,000. After 5 months B joins with ₹20,000. If the profit at the end of the year is ₹16,000, what is B's share?
A invests for 12 months and B for 7. A : B $= 15000 \times 12 : 20000 \times 7 = 180000 : 140000 = 9 : 7$. One part is $16000 \div 16 = 1000$. B gets ₹7,000 and A ₹9,000.
- Months for a late partner = 12 − months before joining.
- Here B's months are 7, not 12.
- Taking B's months as 12 gives 3 : 4 and a wrong answer.
- Subtract the late months from the year.
The ratio of two partners' capitals is $2 : 3$ and the ratio of their times is $5 : 4$. What is the ratio of their profits?
The profit ratio is the ratio of capital × time $= 2 \times 5 : 3 \times 4 = 10 : 12 = 5 : 6$. The option 8 : 15 comes from reversing the times ($2 \times 4 : 3 \times 5$).
- Multiply the same person's capital part and time part.
- Write the product ratio in lowest terms.
- Reversing the time ratio is the commonest slip.
- Capital part × time part, for the same person.
The capitals of A and B are ₹20,000 and ₹30,000. A manages the business and first gets 10% of the total profit as remuneration; the rest is shared in the ratio of capitals. If the profit is ₹15,000, how much does A get in all?
The remuneration is 10% of ₹15,000 = ₹1,500. The remaining ₹13,500 is shared $2 : 3$, so A's part is $13500 \times \frac{2}{5} = 5400$. A's total is $1500 + 5400 =$ ₹6,900. ₹6,000 comes from dividing the full ₹15,000 as 2 : 3.
- Take the remuneration first, then share the rest.
- B gets $13500 \times \frac{3}{5} =$ ₹8,100.
- Splitting the whole ₹15,000 as 2 : 3 gives ₹6,000 for A, which is wrong.
- Salary first, split after.
The ratio of capitals of A, B and C is $1 : 2 : 3$. They invest for 6, 5 and 4 months respectively. If the profit is ₹14,000, what is B's share?
The profit ratio is $1 \times 6 : 2 \times 5 : 3 \times 4 = 6 : 10 : 12 = 3 : 5 : 6$ with sum 14. One part is $14000 \div 14 = 1000$. B gets $5 \times 1000 =$ ₹5,000. A gets ₹3,000 and C ₹6,000.
- Multiply each capital part by its months.
- Divide 6 : 10 : 12 by 2 to get 3 : 5 : 6.
- Check that the sum of the ratio divides the profit neatly.
A invests ₹8,000 for the whole year and B invests ₹12,000 for some months. If their profits are equal, after how many months did B join?
Equal profits mean capital × months are equal. A's product is $8000 \times 12 = 96000$. For B, $12000 \times x = 96000$, so $x = 8$ months. B invested for 8 months, so B joined after $12 - 8 = 4$ months.
- The question asks when B joined, not how long B invested.
- Equate the two products.
- Taking x = 8 as the answer is the usual slip.
- The answer is 12 − 8 = 4, not 8.
The capitals of two partners are in the ratio $5 : 7$ and the time is equal. If A's profit is ₹1,500, what is the total profit?
A's 5 parts are ₹1,500, so one part is ₹300. There are 12 parts in all, so the total profit is $12 \times 300 =$ ₹3,600. B gets $7 \times 300 =$ ₹2,100.
- In reverse questions, find one part first.
- Total parts = 5 + 7 = 12.
- Known share ÷ its ratio part = one part.
A invests ₹6,000 for the whole year. B invests ₹8,000 for the first 6 months and ₹6,000 for the next 6 months. If the profit for the year is ₹6,500, what is A's share?
A's product is $6000 \times 12 = 72000$. B's is $8000 \times 6 + 6000 \times 6 = 48000 + 36000 = 84000$. The ratio is $72 : 84 = 6 : 7$ with sum 13, and one part is $6500 \div 13 = 500$. A gets $6 \times 500 =$ ₹3,000.
- If capital changes, add (money × months) for each period.
- B's total is 84000 and A's is 72000.
- Add period by period.
The capitals of two partners are in the ratio $3 : 4$ and the time is equal. If B's profit is ₹600 more than A's, what is the total profit?
The difference of the ratio, $4 - 3 = 1$ part, is ₹600. There are 7 parts, so the total profit is $7 \times 600 =$ ₹4,200. A gets ₹1,800 and B ₹2,400, a difference of ₹600.
- Use the difference in parts to find one part.
- Total profit = total parts × one part.
- 1 part = ₹600, 7 parts in all.
A, B and C start a business with ₹1,20,000 in all. A invests ₹10,000 more than B and B invests ₹10,000 more than C. If the profit in one year is ₹24,000, what is A's share?
Let C invest $x$, so B invests $x + 10000$ and A invests $x + 20000$. Adding, $3x + 30000 = 120000$, so $x = 30000$. The capitals are A ₹50,000, B ₹40,000 and C ₹30,000, in the ratio $5 : 4 : 3$ with sum 12, so one part is ₹2,000. A gets $5 \times 2000 =$ ₹10,000.
- First find each capital using an equation.
- Then take the ratio and one part.
- Call the smallest x to keep the equation simple.
📊 Topic Analysis
12 practice questions on partnership sums for WBPSC Clerkship 2024 arithmetic, each with a worked explanation.
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