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Partnership Questions with Solutions

Partnership questions extend Ratio and Proportion to shared business profit — the one idea to hold onto is that profit splits by capital × time, not capital alone, whenever partners invest for different durations. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • If all partners invest for the SAME length of time, profit is split simply in the ratio of their capital amounts.
  • If partners invest for DIFFERENT durations, each partner’s share of the ratio is capital × time — this product is what determines the split, not the capital amount on its own.
  • This can produce a non-obvious ratio: a smaller capital invested for much longer can earn an equal or even larger share than a bigger capital invested briefly.
  • For a "working partner" who manages the business and earns an extra fixed fee for that on top of their investment return: subtract the fee from the total profit first, then split only the REMAINDER in the capital × time ratio.

Worked examples

1. 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.

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.

Answer: A gets ₹2,000, B gets ₹3,000

2. 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.

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.

Answer: A gets ₹3,100, B gets ₹3,100

3. 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.

Solution

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

Answer: ₹10,000

4. 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.

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.)

Answer: ₹13,500

Try these yourself

Work through these the same way, then check against the answer.

1. 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.

Answer: P gets ₹3,000, Q gets ₹5,000

2. 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.

Answer: X gets ₹2,000, Y gets ₹3,000

3. 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.

Answer: ₹9,000

Where this comes up

Partnership is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and builds directly on Ratio and Proportion.

Practice more Partnership questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Partnership (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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