Quantitative Aptitude

Partnership: Practice Questions with Answers

14 practice questions on Partnership, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   A invests ₹30,000 at the start of the year. B joins the business after 3 months with ₹45,000. Find the profit-sharing ratio for that year.

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   Answer: 8 : 9

   Solution:

   1. A's money is invested for the full 12 months; B's money is invested only for the remaining 12 − 3 = 9 months.
   2. A: 30,000 × 12 = 3,60,000. B: 45,000 × 9 = 4,05,000.
   3. Ratio A : B = 3,60,000 : 4,05,000 = 8 : 9 (dividing both by 45,000).

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2. Q.2

   A invests ₹40,000 and manages the business, while B invests ₹60,000 as a sleeping partner. A receives 10% of the total profit as a management fee, and the rest is split in the ratio of their capitals. If the total profit is ₹25,000, find B’s total share.

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   Answer: ₹13,500

   Solution:

   1. Management fee (A only) = 10% of 25,000 = ₹2,500. Remaining profit to split = 25,000 − 2,500 = ₹22,500.
   2. Capital ratio A : B = 40,000 : 60,000 = 2 : 3.
   3. B’s share of the remainder = (3/5) × 22,500 = ₹13,500. (B gets no management fee, so this is B’s total share.)

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3. Q.3

   A starts a business with ₹20,000. After 4 months, he adds a further ₹10,000. B joins at the very start with ₹25,000 and keeps it invested for the whole 12-month year. Find the profit-sharing ratio.

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   Answer: 16 : 15

   Solution:

   1. A's capital-months in two stretches: ₹20,000 for the first 4 months, then ₹30,000 for the remaining 8 months.
   2. A: (20,000 × 4) + (30,000 × 8) = 80,000 + 2,40,000 = 3,20,000.
   3. B: 25,000 × 12 = 3,00,000.
   4. Ratio A : B = 3,20,000 : 3,00,000 = 32 : 30 = 16 : 15.

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4. Q.4

   A and B invest in a business for the same time period. Their profits come out in the ratio 4 : 5. If A invested ₹8,000, find B's investment.

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   Answer: ₹10,000

   Solution:

   1. Since the time period is the same for both, the capital ratio equals the profit ratio: A : B = 4 : 5.
   2. 8,000 / B = 4 / 5
   3. B = 8,000 × 5 / 4 = ₹10,000

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5. Q.5

   A invests ₹10,000 for 12 months and B invests ₹15,000 for 8 months in a business. At the end, they earn a profit of ₹6,200. Find each partner’s share.

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   Answer: A gets ₹3,100, B gets ₹3,100

   Solution:

   1. The capitals alone (10,000 vs 15,000) are NOT the ratio to use, since the time periods differ — use capital × time instead.
   2. A: 10,000 × 12 = 1,20,000. B: 15,000 × 8 = 1,20,000. The two products are actually equal, so the ratio is 1 : 1, even though the capitals themselves weren’t equal.
   3. Each partner gets half of ₹6,200 = ₹3,100.

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6. Q.6

   A and B start a business with capitals of ₹8,000 and ₹12,000 respectively, investing for the same time period. At the end of the year, they earn a profit of ₹5,000. Find each partner’s share.

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   Answer: A gets ₹2,000, B gets ₹3,000

   Solution:

   1. Since the time period is the same for both, the ratio is simply the capital ratio: 8,000 : 12,000 = 2 : 3.
   2. A’s share = (2/5) × 5,000 = ₹2,000. B’s share = (3/5) × 5,000 = ₹3,000.

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7. Q.7

   A, B and C invest in a business in the ratio 2 : 3 : 5, for the same time period. If the total profit is ₹20,000, find C’s share.

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   Answer: ₹10,000

   Solution:

   1. Sum of ratio terms = 2 + 3 + 5 = 10.
   2. C’s share = (5/10) × 20,000 = ₹10,000.

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8. Q.8

   P and Q start a business with capitals of ₹15,000 and ₹25,000, investing for the same time period. At the end of the year, they earn a profit of ₹8,000. Find each partner’s share.

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   Answer: P gets ₹3,000, Q gets ₹5,000. Capital ratio 3:5 on a sum of 8.

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9. Q.9

   X starts a business with ₹24,000. Y joins after 4 months with ₹36,000. Find the profit-sharing ratio for the year.

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   Answer: 1 : 1. X: 24,000×12 = 2,88,000; Y: 36,000×8 = 2,88,000.

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10. Q.10

    Two partners invest for the same time period in the ratio 3 : 7. If the total profit is ₹40,000, find each partner's share.

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    Answer: ₹12,000 and ₹28,000. (3/10) and (7/10) of 40,000.

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11. Q.11

    P starts a business with ₹15,000. After 6 months, he withdraws ₹5,000 (leaving ₹10,000 invested). Q joins at the start with ₹12,000 and stays the full year. Find the profit-sharing ratio for the year.

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    Answer: 25 : 24. P: (15,000×6)+(10,000×6) = 1,50,000; Q: 12,000×12 = 1,44,000; divide both by 6,000.

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12. Q.12

    A and B invest for the same time period. Their profits are ₹18,000 and ₹24,000 respectively. If B invested ₹40,000, find A's investment.

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    Answer: ₹30,000. Profit ratio 18,000:24,000 = 3:4 = capital ratio; A = 40,000 × 3/4.

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13. Q.13

    A, B and C invest in a business in the ratio 3 : 4 : 5, for the same time period. If the total profit is ₹36,000, find A’s share.

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    Answer: ₹9,000. (3/12) × 36,000.

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14. Q.14

    X invests ₹12,000 for 4 months and Y invests ₹8,000 for 9 months. If the profit is ₹5,000, find each partner’s share.

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    Answer: X gets ₹2,000, Y gets ₹3,000. Capital-months: X=48,000, Y=72,000, ratio 2:3.

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