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AFCAT Partnership

Study Material — 2 PYQs (2019–2020) · Concept Notes · Shortcuts

AFCAT Partnership is a frequently tested subtopic — 2 previous year questions from 2019–2020 papers are included below with concept notes, key rules and shortcut tricks.

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2019–2020

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Previous Year Questions

AFCAT Partnership — Past Exam Questions

2 questions from actual AFCAT papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

A, B, and C enter into a partnership. A invests ₹45,000 for 8 months, B invests ₹60,000 for 10 months, and C invests ₹50,000 for 12 months. At the end of the year, the profit is ₹47,600. However, B withdraws ₹15,000 after 6 months (reducing his investment). What is A's share of the profit?

Exam Q 22019Previous Year Pattern

A, B, and C enter into a partnership. A invests ₹45,000 for 8 months, B invests ₹60,000 for 10 months, and C invests ₹50,000 for 12 months. At the end of the year, the profit is ₹47,200. However, B withdraws ₹15,000 after 6 months (reducing his investment). What is A's share of the profit?

Concept Notes

Partnership— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

Think of it this way

If you invest more money, or invest for more time, you deserve a bigger share of the profit. That is the entire logic of partnership. --- KEY RULES / PROPERTIES Rule 1 — Simple Partnership: All partners invest for the SAME time period. Profit is divided in the ratio of their investments only

Rule 2 — Compound Partnership

Partners invest for DIFFERENT time periods. Profit is divided in the ratio of (Investment × Time)

Rule 3 — Working Partner vs Sleeping Partner

A working partner actively manages the business. A sleeping partner only invests money. The working partner may get a salary or extra commission first, THEN the remaining profit is split in the investment ratio. ---

2.Formula Block

Memorise — at least one formula appears in every paper

Profit Ratio = Capital of A : Capital of B

Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B)

A's share = (A's ratio unit / Total ratio units) × Total Profit

Remaining Profit = Total Profit − Salary of Working Partner

Simple Partnership:

Compound Partnership:

If A gets Rs. X out of total profit P:

Working Partner formula:

Then split remaining profit in capital ratio.

---

3.Exam Patterns

What examiners ask — read before attempting PYQs

— WHAT GETS ASKED SSC CGL asks partnership in 3 main ways: 1. Find one partner's share when total profit is given. 2. Find total profit when one partner's share is given. 3. One partner joins later — find profit ratio (compound partnership). 4.

Working partner gets a fixed salary — find individual shares. ---

4.Shortcuts

Use these to save 30–60 seconds per question

Trick 1 — Monthly Equivalent Method

Always convert investment to 'Rupee-Months' (Capital × Months). This works for ALL cases, simple or compound

Example

Rs. 6000 for 4 months = 6000 × 4 = 24000 rupee-months

Trick 2 — One Partner Joins Late

If A starts from month 1 and B joins after 'n' months, and total period is T months: A's effective capital = Capital_A × T B's effective capital = Capital_B × (T − n) Trick 3 — Ratio Shortcut for Same Capital: If capitals are equal, profit ratio = ratio of time periods directly. No multiplication needed. ---

5.Worked Example

Solve this step-by-step before moving on

1

Step 1

Profit Ratio = 5000 : 8000 = 5 : 8

2

Step 2

Total parts = 5 + 8 = 13

3

Step 3

B's share = (8/13) × 3900 = Rs. 2400 Answer: B gets Rs. 2400. --- WORKED EXAMPLE 2 — Compound Partnership (Late Joining) Question: A starts a business with Rs. 12000. After 4 months, B joins with Rs. 18000. At year end, total profit is Rs. 11000. Find each partner's share.

1

Step 1

Time for A = 12 months, Time for B = 12 − 4 = 8 months

2

Step 2

A's rupee-months = 12000 × 12 = 144000

3

Step 3

B's rupee-months = 18000 × 8 = 144000

4

Step 4

Profit Ratio = 144000 : 144000 = 1 : 1

5

Step 5

A's share = B's share = 11000 / 2 = Rs. 5500 each Answer: Each partner gets Rs. 5500. Note: Even though B invested more money, joining late made the ratio equal. This surprises many students! ---

6.Exam Traps

Common mistakes students make — avoid these

— THE NUMBER 1 TRAP Students forget to multiply capital by time when partners join at different times. They directly do: 12000 : 18000 = 2 : 3 (WRONG!) Always check: Are the time periods same or different? If different → MUST use Capital × Time for every partner. This mistake alone causes maximum wrong answers in partnership questions.

Key Points to Remember

Partnership profit is shared in the ratio of (Capital × Time) for each partner.
Simple Partnership: All partners invest for equal time — use capital ratio directly.
Compound Partnership: Partners invest for different durations — always multiply Capital × Time.
Formula: Profit Share of A = [A's (Capital × Time) / Total (Capital × Time)] × Total Profit.
If B joins 'n' months late in a T-month business, B's time = T − n months.
Working partner gets salary first; remaining profit is then split in capital ratio.
If capitals are equal, profit ratio equals the ratio of time periods only.
Shortcut: Convert all investments to Rupee-Months to solve any partnership problem.
Sleeping partner only invests money; working partner manages — working partner can claim extra salary.
Trap: Never compare capitals directly when time periods are different — always apply Capital × Time.

Exam-Specific Tips

In a compound partnership, Profit Ratio = (Capital_A × Time_A) : (Capital_B × Time_B).
If A invests Rs. P for the whole year and B invests Rs. Q for only 6 months, B's effective capital is Q/2 of A's equivalent on a 12-month basis.
A working partner's salary or commission is deducted from TOTAL profit BEFORE dividing the remaining profit.
If two partners invest equal amounts but for different durations, profit ratio equals ratio of their time periods.
In SSC CGL, the most frequently tested partnership variant is 'one partner joins later' (compound partnership with late entry).
If three partners A, B, C invest in ratio a:b:c for times t1:t2:t3, profit ratio = at1 : bt2 : ct3.
A partner who re-invests or withdraws capital mid-year must have separate Capital × Time calculated for each phase and then added.

Practice MCQs

Partnership — Practice Questions

37graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 37

All MCQs →

Practice 1easy

A and B enter into a partnership. A invests ₹4,500 and B invests ₹5,500. After one year, the profit is ₹2,000. What is A's share of the profit?

Practice 2easy

X, Y, and Z start a business with investments in the ratio 3 : 4 : 5. If the total profit at the end of the year is ₹24,000, what is Z's profit share?

Practice 3easy

Two partners, M and N, invest capital in the ratio 3:4. They agree to share profits in the same ratio. If M's profit is ₹1,200, what is the total profit?

Practice 4easy

A and B enter into a partnership. A invests ₹4,500 and B invests ₹5,500. After one year, the profit is ₹2,000. What is B's share of the profit?

Practice 5easy

X and Y started a business with investments in the ratio 4:5. After one year, the profit earned is ₹18,000. If X's share of profit is ₹8,000, find Y's investment if X's investment was ₹40,000.

Practice 6easy

A and B enter into a partnership with capital investments of ₹15,000 and ₹25,000 respectively. If the profit at the end of the year is ₹8,000, what is B's share of the profit?

Practice 7easy

A, B, and C invest ₹15,000, ₹20,000, and ₹25,000 respectively for equal time periods. The profit earned is ₹12,000. What is the difference between C's and A's profit shares?

Practice 8easy

Three partners A, B, and C invested capital in the ratio 3:4:5 and their profits were in the ratio 6:8:10. If the total profit is ₹5,400, what is C's profit?

Practice 9easy

A and B form a partnership where A invests ₹60,000 for 12 months and B invests ₹80,000 for 9 months. If the total profit is ₹7,900, what is A's share of the profit?

Practice 10easy

M and N entered into a partnership. M invested ₹50,000 for the entire year, while N invested ₹75,000 but only for 8 months. The profit earned is ₹13,000. What is N's share of the profit?

Practice 11easy

X, Y, and Z form a partnership with capital contributions in the ratio 2:3:5. If the total profit at the end of the year is ₹5,000, how much profit does Z receive?

Practice 12easy

P and Q form a partnership. P invests ₹20,000 for 12 months and Q invests ₹25,000 for 8 months. If the profit is ₹11,000, how much profit does P receive?

Practice 13easy

P, Q, and R invested ₹20,000, ₹30,000, and ₹50,000 respectively in a partnership. The profit at the end of the year is ₹20,000. How much more profit does R get compared to P?

Practice 14easy

In a partnership, A and B's profit shares are in the ratio 3:2. If A's profit is ₹4,500, what is the total profit?

Practice 15easy

M and N invest capital in the ratio 5:7. They agree to share profits in the same ratio. If N receives ₹3,500 as profit, how much does M receive?

Practice 16easy

X, Y, and Z form a partnership with capital contributions in the ratio 2:3:5. If the total profit at the end of the year is ₹5,000, what is Z's profit share?

Practice 17easy

Three partners A, B, and C invest ₹2,000, ₹3,000, and ₹5,000 respectively. The profit is ₹3,000. If the profit is distributed equally among all three instead of by investment ratio, how much more does A receive?

Practice 18easy

A and B enter into a partnership. A invests ₹12,000 and B invests ₹18,000. After one year, the profit is ₹9,000. What is A's share of the profit?

Practice 19medium

Three partners A, B, and C invest capital in the ratio 3:4:5 and their profits are in the ratio 6:8:10. If A's investment period is 12 months, what is the ratio of B's investment period to C's investment period?

Practice 20medium

P and Q start a business with investments in the ratio 5:7. After 6 months, P withdraws half of his capital and Q adds 50% more to his capital. If the profit at the end of the year is ₹2,400, what is Q's profit share?

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60-Second Revision — Partnership

Formula: Profit Ratio = Capital × Time for each partner. Always use this — never skip the time factor.
Trap: If partners join at different times, NEVER split profit using capital ratio alone. Multiply by time first.
Rule: Working partner gets salary deducted from total profit first, then remaining profit splits by capital ratio.
Shortcut: Convert everything to Rupee-Months. Add phases if capital changes mid-year.
Remember: Equal capitals → profit ratio = time ratio directly. Equal time → profit ratio = capital ratio directly.
Late joining formula: If B joins after n months in a T-month year, B's time = T − n months.
Check question type first: Same time period (simple) or different time period (compound) — this decides your method.

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