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Partnership & Selling Price Adjustments

Introduction

In business-related aptitude problems, two common themes appear: Partnerships (where two or more people invest money and share profits) and Selling Price Adjustments (where the selling price changes due to discounts or markups).

This pattern is important because it tests both profit-sharing logic and pricing adjustments, which often appear together in competitive exams.

Pattern: Partnership & Selling Price Adjustments

Pattern

Partnership: Profit is shared in the ratio of (Capital × Time).

Selling Price Adjustments: SP = CP × (1 ± % adjustment).

Step-by-Step Example

Question

A and B start a business by investing ₹40,000 and ₹60,000 respectively. After a year, they earn a profit of ₹30,000. Meanwhile, they sold a product whose cost price was ₹500. If they sold it at 20% profit but later gave a 10% discount on the marked price, find: 1. A’s share of the profit. 2. The selling price of the product after discount.

Options:

  • A. ₹12,000 and ₹540
  • B. ₹10,000 and ₹500
  • C. ₹14,000 and ₹600
  • D. ₹12,000 and ₹500

Solution

  1. Step 1: Calculate the partnership ratio

    A:B = 40,000 : 60,000 = 2 : 3

  2. Step 2: Compute A’s share from total profit

    Total profit = ₹30,000
    A’s share = (2/5) × 30,000 = ₹12,000
    B’s share = (3/5) × 30,000 = ₹18,000

  3. Step 3: Find the marked price from CP

    CP = ₹500
    Markup = 20%
    Marked Price = 500 × 1.2 = ₹600

  4. Step 4: Apply discount

    Discount = 10% of 600 = ₹60
    SP = 600 - 60 = ₹540

  5. Final Answer:

    A’s share = ₹12,000; Selling Price after discount = ₹540 → Option A

  6. Quick Check:

    2:3 ratio → 12,000 + 18,000 = 30,000 ✅
    SP > CP → Profit still maintained (540 > 500) ✅

Quick Variations

1. Different time durations for partners (investment × time).

2. Multiple or successive discounts on MP.

3. Mark-up and discount flow: CP → MP → SP.

Trick to Always Use

  • Partnership: Profit share = (Capital × Time) ÷ Total.
  • Price Adjustments: First compute MP from CP, then apply discount.

Summary

Summary

  • Partnership profit-sharing uses the investment × time method.
  • Selling price adjustments follow CP → MP → SP.
  • Reverse-checking ensures consistency: SP + Discount = MP → MP compared with CP confirms profit/loss.
  • Both concepts commonly appear together in business maths problems.

Example to remember:
₹12,000 share & ₹540 discounted SP

Practice

(1/5)
1. A and B invest ₹20,000 and ₹30,000 in a business. After a year they earn a profit of ₹25,000. Find A’s share of the profit.
easy
A. ₹10,000
B. ₹12,000
C. ₹15,000
D. ₹20,000

Solution

  1. Step 1: Convert capital to ratio

    A:B = 20,000 : 30,000 = 2 : 3.

  2. Step 2: Add ratio parts

    Total parts = 2 + 3 = 5.

  3. Step 3: Compute A’s profit share

    A’s share = (2/5) × 25,000 = ₹10,000.

  4. Final Answer:

    ₹10,000 → Option A

  5. Quick Check:

    B’s share = (3/5) × 25,000 = 15,000 → 10,000 + 15,000 = 25,000 (matches total profit) ✅
Hint: Convert investments into a ratio, then multiply by total profit.
Common Mistakes: Sharing profit equally instead of by investment ratio.
2. A shopkeeper buys an article at ₹400. He marks it 25% above cost and then allows a 20% discount on the marked price. Find the selling price.
easy
A. ₹380
B. ₹400
C. ₹420
D. ₹450

Solution

  1. Step 1: Calculate marked price

    MP = 400 × 1.25 = ₹500.

  2. Step 2: Apply discount

    Discount = 20% of 500 = ₹100.

  3. Step 3: Find selling price

    SP = 500 - 100 = ₹400.

  4. Final Answer:

    ₹400 → Option B

  5. Quick Check:

    SP = CP → No profit/loss → Correct consistency check! ✅
Hint: Always compute MP first (using markup), then subtract discount to get SP.
Common Mistakes: Applying discount on CP instead of MP.
3. A trader marks goods at 40% above cost price. He offers a 20% discount on the marked price. If cost price is ₹600, find the selling price.
easy
A. ₹682
B. ₹700
C. ₹720
D. ₹672

Solution

  1. Step 1: Calculate marked price

    MP = 600 × 1.4 = ₹840.

  2. Step 2: Apply discount

    Discount = 20% of 840 = ₹168.

  3. Step 3: Find selling price

    SP = 840 - 168 = ₹672.

  4. Final Answer:

    ₹672 → Option D

  5. Quick Check:

    Profit = 72 → 72 is 12% of 600 → consistent with SP > CP ❤️
Hint: Apply markup on CP to get MP, then compute discount on MP.
Common Mistakes: Subtracting discount percent directly from CP instead of MP.
4. C invests ₹50,000 for 1 year while D invests ₹70,000 for 8 months. They earn a profit of ₹29,000. Find D’s share.
medium
A. ₹16,000
B. ₹12,000
C. ₹14,000
D. ₹15,000

Solution

  1. Step 1: Convert investment to capital×time

    C = 50,000 × 12 = 6,00,000; D = 70,000 × 8 = 5,60,000.

  2. Step 2: Form ratio

    C:D = 6,00,000 : 5,60,000 = 15 : 14.

  3. Step 3: Compute D’s share

    D’s share = (14/29) × 29,000 = ₹14,000.

  4. Final Answer:

    ₹14,000 → Option C

  5. Quick Check:

    C’s share = 15,000 → 15,000 + 14,000 = 29,000 (correct) ✅
Hint: Multiply each capital by its duration before forming the ratio.
Common Mistakes: Using capital ratio only and ignoring time differences.
5. E invests ₹60,000 for 1 year while F invests ₹40,000 for 6 months. If total profit is ₹24,000, find F’s share.
medium
A. ₹6,000
B. ₹8,000
C. ₹10,000
D. ₹12,000

Solution

  1. Step 1: Convert each to capital×time

    E = 60,000 × 12 = 7,20,000; F = 40,000 × 6 = 2,40,000.

  2. Step 2: Form ratio

    E:F = 3 : 1.

  3. Step 3: Compute F’s share

    F’s share = (1/4) × 24,000 = ₹6,000.

  4. Final Answer:

    ₹6,000 → Option A

  5. Quick Check:

    E’s share = 18,000 → 18,000 + 6,000 = 24,000 → correct! ✅
Hint: Always convert to capital×time before forming the ratio.
Common Mistakes: Ignoring time or mixing months and years.

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