What is Topic 5 in GAT Pakistan?

Topic 5 is a topic in the ('quantitative-techniques', 'Quantitative Techniques') syllabus of GAT Pakistan. It carries a weight of 3% in the exam. Our notes cover the key concepts, formulas, and problem-solving approaches you need to master this topic.

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Profit and Loss

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Profit and Loss — Key Facts for GAT Pakistan

Basic Formulas:

Term	Formula
Profit	SP - CP (when SP > CP)
Loss	CP - SP (when CP > SP)
Profit %	(Profit/CP) × 100
Loss %	(Loss/CP) × 100
Selling Price (Profit)	CP × (1 + r/100)
Selling Price (Loss)	CP × (1 - r/100)
Cost Price (Profit)	SP/(1 + r/100)
Cost Price (Loss)	SP/(1 - r/100)

Quick Reference Table:

Discount/Profit	Multiplier (SP from CP)
10% profit	1.10
20% profit	1.20
25% profit	1.25
50% profit	1.50
10% loss	0.90
20% loss	0.80
50% loss	0.50

⚡ GAT Exam Tip: Always calculate profit/loss as percentage of COST PRICE, not selling price!

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Profit and Loss — Detailed Study Guide

Basic Calculations

Worked Examples:

Example 1: A shopkeeper buys a shirt for Rs. 400 and sells for Rs. 500.
Find profit percentage.

Solution:
CP = Rs. 400, SP = Rs. 500
Profit = 500 - 400 = Rs. 100
Profit % = (100/400) × 100 = 25%

Example 2: A merchant sells a watch for Rs. 1,800 at a loss of 10%.
What was the cost price?

Solution:
SP = Rs. 1800, Loss = 10%
CP = SP/(1 - Loss/100) = 1800/(1 - 0.10) = 1800/0.90 = Rs. 2000

Example 3: If marked price is Rs. 500 and discount is 20%, find selling price.

Solution:
Discount = 20% of 500 = Rs. 100
SP = MP - Discount = 500 - 100 = Rs. 400

Or: SP = MP × (1 - d/100) = 500 × 0.80 = Rs. 400

Discount and Marked Price

Relationship Between MP, CP, and SP:

Example: A trader offers 20% discount on marked price and still makes
15% profit. If the cost price is Rs. 800, find the marked price.

Solution:
CP = Rs. 800, Profit = 15%
SP = CP × 1.15 = 800 × 1.15 = Rs. 920

SP = MP × (1 - Discount/100)
920 = MP × 0.80
MP = 920/0.80 = Rs. 1150

Answer: Marked Price = Rs. 1150

⚡ Common Mistake: Students often confuse discount percentage with profit percentage. Discount is always on Marked Price!

False Weights and Business Tricks

Problem Types:

Example 1: A shopkeeper uses a false weight of 900g when he should use 1000g.
If he sells at cost price, find his profit percentage.

Solution:
He gives 900g but charges for 1000g
CP of 900g = Cost of 900g (sold as 1000g at same rate)
SP of 900g (sold as 1000g) = Cost of 1000g

Profit = 1000 - 900 = 100 on 900
Profit % = (100/900) × 100 = 11.11%

Example 2: A merchant sells at cost price but uses 800g weight instead of
1kg. Find his gain percent.

Solution:
Profit = (1000 - 800)/800 × 100 = 25%

⚡ GAT PYQ: “A shopkeeper makes a 20% profit by selling goods at 10% discount on his marked price. If the cost price is Rs. 500, find the marked price.” → Answer: Rs. 666.67

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Profit and Loss — Complete Notes for GAT

Successive Transactions

Two Profits/Losses:

Example: A merchant buys goods at 20% discount on MP and sells at
marked price. Find profit percentage.

Solution:
Let MP = Rs. 100
CP = 80% of 100 = Rs. 80
SP = Rs. 100 (at marked price)
Profit = 100 - 80 = Rs. 20
Profit % = (20/80) × 100 = 25%

Profit and Discount Combination:

Example: A shopkeeper gives two successive discounts of 20% and 10%
on an article marked at Rs. 1000. If his cost is Rs. 700, find
profit/loss.

Solution:
After 20% discount: 1000 × 0.80 = Rs. 800
After 10% discount: 800 × 0.90 = Rs. 720
SP = Rs. 720
CP = Rs. 700
Profit = Rs. 20
Profit % = (20/700) × 100 = 2.86%

Break-Even and Multiple Transactions

Break-Even Point:

Example: A shopkeeper sells an article at Rs. 600 and loses 20%.
At what price should he sell to break even?

Solution:
SP = Rs. 600, Loss = 20%
CP = 600/(1 - 0.20) = 600/0.80 = Rs. 750
Break-even means SP = CP
So he should sell at Rs. 750

Finding Original Cost from Successive Changes:

Example: After two successive increases of 10% and 20%, the price
becomes Rs. 660. Find the original price.

Solution:
Let CP = x
After 10% increase: x × 1.10
After 20% increase: x × 1.10 × 1.20 = 1.32x
1.32x = 660
x = 660/1.32 = Rs. 500

GAT-Style Practice Questions

1. A shopkeeper buys a cycle for Rs. 1500 and sells at 15% profit.
   What is the selling price?
   (a) Rs. 1650 (b) Rs. 1725 (c) Rs. 1700 (d) Rs. 1750

   Answer: (b) Rs. 1725
   Solution: SP = 1500 × (1 + 15/100) = 1500 × 1.15 = Rs. 1725

2. A trader sells an article at Rs. 920 at a loss of 8%. Find cost price.
   (a) Rs. 1000 (b) Rs. 980 (c) Rs. 1050 (d) Rs. 1080

   Answer: (a) Rs. 1000
   Solution: CP = 920/(1 - 8/100) = 920/0.92 = Rs. 1000

3. The marked price of a radio is Rs. 800. It is sold at a discount of 15%.
   If the shopkeeper makes a profit of 19%, find the cost price.
   (a) Rs. 550 (b) Rs. 600 (c) Rs. 650 (d) Rs. 700

   Answer: (b) Rs. 600
   Solution: SP = 800 × 0.85 = Rs. 680
             CP = 680/1.19 = Rs. 571.4... ≈ Rs. 600

4. A shopkeeper sells two watches at Rs. 600 each. On one he gains 20%
   and on the other he loses 20%. Find net profit/loss.
   (a) No profit no loss (b) Rs. 40 loss (c) Rs. 50 gain (d) Rs. 60 loss

   Answer: (c) 4% loss
   Solution:
   Watch 1: SP = 600, Profit 20%
            CP = 600/1.20 = Rs. 500
            
   Watch 2: SP = 600, Loss 20%
            CP = 600/0.80 = Rs. 750
            
   Total CP = 500 + 750 = Rs. 1250
   Total SP = 600 + 600 = Rs. 1200
   Loss = 1250 - 1200 = Rs. 50
   Loss % = (50/1250) × 100 = 4%

5. A shopkeeper offers 3 successive discounts of 10%, 20%, and 5% on
   an article marked at Rs. 1000. Find the final selling price.
   (a) Rs. 684 (b) Rs. 720 (c) Rs. 750 (d) Rs. 700

   Answer: (a) Rs. 684
   Solution: After 10%: 1000 × 0.90 = 900
             After 20%: 900 × 0.80 = 720
             After 5%: 720 × 0.95 = Rs. 684

⚡ GAT Strategy: For multiple successive discounts, multiply the remaining factors. For “no profit no loss” problems, set up equations with CP = SP.

Example: A invests Rs. 5000 for 4 months, B invests Rs. 8000 for 6 months.
They earn a profit of Rs. 3800. Find profit share.

Solution:
A's contribution = 5000 × 4 = Rs. 20,000
B's contribution = 8000 × 6 = Rs. 48,000
Total = Rs. 68,000

A's share = (20000/68000) × 3800 = Rs. 1117.65
B's share = (48000/68000) × 3800 = Rs. 2682.35

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