How to Solve Partnership Problems

How to Solve Partnership Problems

(For SSC, Bank, Railway Exams – Ace Your Quant Section!)

Introduction

"Partnership problems decide 3–5 marks in every SSC, Bank, and Railway exam—miss them, and you lose easy marks. Master this in 30 minutes, and you’ll solve them faster than the clock ticks!

(On camera: Hold up a past paper with a highlighted partnership question.) "This one question could be the difference between Tier-1 qualification and a reattempt. Let’s break it down—step by step."

What You Need To Know First

Before diving in, ensure you’re comfortable with: 1. Ratio and Proportion – Splitting quantities in given ratios. 2. Basic Profit/Loss – Understanding terms like investment, profit, loss. 3. Time Calculations – Multiplying investment by time (e.g., ₹1000 for 6 months = ₹6000-months).

(On camera: Pause, ask students to nod if they’re confident with these.) "If any of these feel shaky, pause now and review them—this guide assumes you’ve got these locked down."

Key Vocabulary

(On camera: Point to each term, read aloud, and ask students to repeat the example.) "These terms will pop up in every question. Memorize them now—no excuses!

Formulas To Know

1. Profit-Sharing Ratio (When Time is Equal)

Formula: Profit Ratio = Investment₁ : Investment₂ : Investment₃

Variables: - Investment₁ = Money invested by Partner 1 - Investment₂ = Money invested by Partner 2

MEMORISE THIS – Used in 70% of partnership questions.

2. Profit-Sharing Ratio (When Time is Different)

Formula: Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂) : (Investment₃ × Time₃)

Variables: - Time₁ = Duration (in months/years) Partner 1’s money was invested.

MEMORISE THIS – The most important formula for this topic.

3. Calculating Individual Profit

Formula: Partner’s Share = (Partner’s Ratio Part / Total Ratio) × Total Profit

Example: If ratio = 3:2 and total profit = ₹5000, A’s share = (3/5) × ₹5000 = ₹3000.

MEMORISE THIS – You’ll use this in every question.

(On camera: Write formulas on a whiteboard, underline "MEMORISE THIS.") "These three formulas are your weapons. Write them down now—no peeking later!

Step-by-Step Method

Follow these exact steps for every partnership problem:

1. Read the question carefully. Underline:
2. Investments of each partner.
3. Time periods (if given).

4. Total profit/loss.

5. Check if time is involved.

6. If no time → Use Profit Ratio = Investment₁ : Investment₂.

7. If time is given → Use (Investment × Time)₁ : (Investment × Time)₂.

8. Calculate the ratio.

9. Simplify the ratio (e.g., 10:6 → 5:3).

10. Find the total parts of the ratio.

11. Add all parts (e.g., 5 + 3 = 8).

12. Calculate each partner’s share.

13. (Partner’s Part / Total Parts) × Total Profit.

14. Verify your answer.

15. Add all shares → Should equal total profit.

(On camera: Demonstrate each step with hand gestures—e.g., "Step 2: Time? Yes or no?") "Stick to these steps like a checklist. No shortcuts—examiners love to trick you!

Worked Example Using Steps

Question: A and B start a business. A invests ₹4000 for 6 months. B invests ₹6000 for 4 months. Total profit = ₹2500. Find B’s share.

Step-by-Step Solution:

1. Underline key info:
2. A: ₹4000 for 6 months.
3. B: ₹6000 for 4 months.

4. Total profit = ₹2500.

5. Time is involved → Use (Investment × Time) formula.

6. A’s part = 4000 × 6 = 24,000.

7. B’s part = 6000 × 4 = 24,000.

8. Ratio = 24,000 : 24,000 = 1:1.

9. Total parts = 1 + 1 = 2.

10. B’s share = (1/2) × ₹2500 = ₹1250.

11. Verify: A’s share = ₹1250. Total = ₹1250 + ₹1250 = ₹2500. ✔️

Answer: B’s share = ₹1250.

(On camera: Write each step on the board, pause after Step 3 to ask, "What’s the ratio?") "See how the steps keep you from making mistakes? Now let’s try harder ones."

Worked Examples

Example 1 – Basic (No Time)

Question: X and Y invest ₹3000 and ₹5000 respectively. Total profit = ₹4000. Find Y’s share.

Solution: 1. No time given → Profit Ratio = Investment₁ : Investment₂. 2. Ratio = 3000 : 5000 = 3:5. 3. Total parts = 3 + 5 = 8. 4. Y’s share = (5/8) × ₹4000 = ₹2500.

What we did and why: - Since time wasn’t mentioned, we used the simpler ratio formula. - Always simplify the ratio first (3000:5000 → 3:5).

Example 2 – Medium (Time Involved)

Question: P, Q, and R invest ₹2000, ₹3000, and ₹4000 for 12, 8, and 6 months respectively. Total profit = ₹10,000. Find Q’s share.

Solution: 1. Time is given → Use (Investment × Time). 2. P’s part = 2000 × 12 = 24,000.
Q’s part = 3000 × 8 = 24,000.
R’s part = 4000 × 6 = 24,000. 3. Ratio = 24,000 : 24,000 : 24,000 = 1:1:1. 4. Total parts = 1 + 1 + 1 = 3. 5. Q’s share = (1/3) × ₹10,000 = ₹3333.33.

What we did and why: - Multiplied each investment by its time to get the ratio. - Even if numbers seem equal, always calculate to avoid traps.

Example 3 – Exam-Style (Disguised Question)

Question: A starts a business with ₹5000. After 3 months, B joins with ₹8000. After 6 more months, C joins with ₹10,000. At the end of the year, profit = ₹20,000. Find C’s share.

Solution: 1. Calculate time for each:
- A: 12 months (full year).
- B: 12 - 3 = 9 months.
- C: 12 - (3 + 6) = 3 months.

1. Use (Investment × Time):
2. A’s part = 5000 × 12 = 60,000.
3. B’s part = 8000 × 9 = 72,000.

4. C’s part = 10,000 × 3 = 30,000.

5. Ratio = 60,000 : 72,000 : 30,000.
   Simplify: Divide by 6000 → 10:12:5.

6. Total parts = 10 + 12 + 5 = 27.

7. C’s share = (5/27) × ₹20,000 ≈ ₹3703.70.

What we did and why: - The question hides the time periods—always calculate them first! - Simplifying the ratio (60,000:72,000:30,000 → 10:12:5) saves time.

(On camera: Emphasize Step 1—"Time is the trick here!) "Examiners love to bury time details. Circle them immediately!

Common Mistakes

(On camera: Hold up a red pen, circle each mistake.) "These mistakes cost marks. Avoid them like a bad investment!

Exam Traps

(On camera: Dramatically point to each trap.) "Examiners set these traps to waste your time. Spot them early, and you’ll finish faster!

1-Minute Recap

"Okay, listen up—this is your 30-second cheat sheet for partnership problems:

1. Two formulas only:
2. No time? Profit Ratio = Investment₁ : Investment₂.

3. Time given? (Investment × Time)₁ : (Investment × Time)₂.

4. Steps to follow:

5. Underline investments, time, and total profit.
6. Calculate the ratio (simplify it!).

7. Add the parts, then find each share.

8. Watch out for:

9. Hidden time periods (draw a timeline!).
10. Different units (convert to months).

11. Not simplifying ratios (big numbers = mistakes).

12. Practice 3 questions tonight:

13. One with no time.
14. One with time.
15. One with a tricky timeline.

That’s it. You’ve got this. Go ace that exam!

(On camera: Smile, give a thumbs-up.) "Now go solve some problems—and don’t forget to simplify those ratios!