8. Partnership and shares
Free study material · concepts, shortcuts & solved questions
In a partnership, profit share is proportional to capital × time. If A invests 5000 for 12 months and B invests 8000 for 6 months, their ratio is 60000:48000=5:4. If partners enter or withdraw at different times, use months or days consistently.
Method before formula Separate capital ratio from time ratio. A sleeping partner may receive a fixed salary first if the question states it; distribute the residual profit according to the agreed rule. |
Formula and decision table
Case | Ratio |
Equal time | Share follows capital |
Equal capital | Share follows time |
Different both | Capital × duration |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
A invests 5000 for 12 months, B 8000 for 6 months. Ratio: | Products are 60000:48000=5:4. | A. 5:4 |
Profit 9000 in ratio 2:1. First share: | First share=9000×2/3=6000. | C. 6000 |
A partner’s capital-time product is used to find: | It determines proportional partnership share. | B. Profit share |
What an examiner is testing
The options around Partnership and shares usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: A invests 5000 for 12 months, B 8000 for 6 months. Ratio: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 5:4, because Products are 60000:48000=5:4.
Example 2: Profit 9000 in ratio 2:1. First share: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 6000, because First share=9000×2/3=6000.
Example 3: A partner’s capital-time product is used to find: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is Profit share, because It determines proportional partnership share.
Chapter practice
1. A invests 5000 for 12 months, B 8000 for 6 months. Ratio:
(A) 5:4 (B) 4:5 (C) 5:8 (D) 8:5
Answer: A. 5:4 | Explanation: Products are 60000:48000=5:4.
2. Profit 9000 in ratio 2:1. First share:
(A) 3000 (B) 4500 (C) 6000 (D) 7500
Answer: C. 6000 | Explanation: First share=9000×2/3=6000.
3. A partner’s capital-time product is used to find:
(A) Average (B) Profit share (C) Discount (D) Speed
Answer: B. Profit share | Explanation: It determines proportional partnership share.
SSC CGL speed and trap clinic
For Partnership and shares, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Partnership and shares? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Partnership and shares question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |