SSC CGL Profit & Loss: Dishonest Dealer & Successive Discount 10-Second Formulas
Category: SSC | Subject: Quantitative Aptitude | Topic: Profit, Loss and Discount | Read Time: 5 min
Master false-weight ratios, successive markups, and net profit percentage problems in under 10 seconds with TCS iON shift derivations.
Key Formulas & 10-Second Reference Table
| Concept / Case | Formula / Rule | When to Use |
|---|---|---|
| Dishonest Dealer (False Weight at Cost Price) | Profit % = [(True Weight - False Weight) / False Weight] × 100 | Shopkeeper claims to sell at Cost Price but uses a lighter weight (e.g. 800g instead of 1000g). |
| Combined Markup + False Weight | SP/CP Ratio = (100 + Markup%) / 100 × (True Weight / False Weight) | Shopkeeper marks up price by x% AND uses false weight simultaneously. |
| Two Successive Discounts (a% and b%) | Net Discount % = a + b - (a × b) / 100 | Two sequential percentage discounts are applied on Marked Price. |
| CP to MP Direct Ratio (No Loss / Profit p% after Discount d%) | CP : MP = (100 - Discount%) : (100 + Profit%) | Question gives discount % on MP and desired profit % on CP. |
Why Dishonest Dealer Questions Decide SSC CGL Tier-1 & Tier-2 Ranks
Every SSC CGL and CHSL cycle features 2 to 3 questions on Profit, Loss, and Discount. The multiplier ratio method eliminates algebraic equations by converting every percentage change and weight manipulation into a single fraction.
- Always place what leaves the shopkeeper's pocket (False Weight) in the denominator.
- Always place what the customer pays for (Claimed Weight) in the numerator.
- Multiply consecutive ratios left-to-right to get the final SP/CP ratio in one line.
The 10-Second Multiplier Chain Method
When a problem combines three operations — such as a 20% markup, a 10% discount, and using 900g instead of 1kg — write the three fractions side by side: (120/100) × (90/100) × (1000/900) = 6/5 × 9/10 × 10/9 = 6/5 = +20% profit.
- 20% Markup → 6/5
- 10% Discount → 9/10
- 900g for 1000g → 10/9
- Product = (6/5) × (9/10) × (10/9) = 6/5 → 20% Net Profit
Solved Exam Questions & Derivations
Solved Example 1: A dishonest dealer professes to sell his goods at a 10% loss on cost price, but uses a weight of 750 grams instead of 1 kg. Find his actual profit percentage.
- (A) 15%
- (B) 20%
- (C) 25%
- (D) 16.67%
Verified Answer: Option (B): 20%
10-Second Shortcut: Multiply price ratio (90/100) by weight ratio (1000/750): (9/10) × (4/3) = 12/10 = +20% profit.
- Price factor for 10% loss = 90/100 = 9/10.
- Weight factor for giving 750g instead of 1000g = 1000/750 = 4/3.
- Net SP/CP = (9/10) × (4/3) = 36/30 = 6/5.
- Profit % = ((6 - 5) / 5) × 100 = 20%.
Solved Example 2: A trader marks his goods 40% above cost price and allows a discount of 25%. What is his net gain percentage?
- (A) 5%
- (B) 10%
- (C) 12%
- (D) 15%
Verified Answer: Option (A): 5%
10-Second Shortcut: Use successive change: +40 - 25 - (40 × 25)/100 = 15 - 10 = +5%.
- Assume Cost Price (CP) = ₹100.
- Marked Price (MP) at 40% markup = ₹140.
- Selling Price (SP) after 25% discount = 140 × (3/4) = ₹105.
- Net Gain = ₹105 - ₹100 = 5%.
Frequently Asked Questions
- Why is False Weight placed in the denominator when calculating dishonest dealer profit?
- Profit percentage is always calculated on actual cost incurred. Since the shopkeeper only parts with the false weight (e.g. 800g), the cost of 800g is his true Cost Price.
- Can the successive percentage formula a + b + ab/100 be used for weight manipulation?
- Yes, provided you first convert the weight manipulation into an equivalent gain percentage [(True - False)/False × 100], though multiplying fractions directly is faster and avoids decimals.
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