---
title: "SSC CGL Profit & Loss: Dishonest Dealer & Successive Discount 10-Second Formulas"
canonical_url: "https://testx.in/guides/ssc-cgl-profit-and-loss-dishonest-dealer-shortcut-formulas"
category: "SSC"
subject: "Quantitative Aptitude"
topic: "Profit, Loss and Discount"
published_at: "2026-11-04"
updated_at: "2026-11-04"
read_time_minutes: 5
cite_as: "TestX Study Guide — SSC CGL Profit & Loss: Dishonest Dealer & Successive Discount 10-Second Formulas: https://testx.in/guides/ssc-cgl-profit-and-loss-dishonest-dealer-shortcut-formulas"
---
# SSC CGL Profit & Loss: Dishonest Dealer & Successive Discount 10-Second Formulas
> Master false-weight ratios, successive markups, and net profit percentage problems in under 10 seconds with TCS iON shift derivations.
- **Category**: SSC | **Subject**: Quantitative Aptitude | **Topic**: Profit, Loss and Discount
- **Read Time**: 5 min | **Updated**: 2026-11-04
- **Canonical URL**: https://testx.in/guides/ssc-cgl-profit-and-loss-dishonest-dealer-shortcut-formulas
## 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 & 10-Second Shortcuts

### 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.
**Step-by-Step Derivation**:
1. Price factor for 10% loss = 90/100 = 9/10.
2. Weight factor for giving 750g instead of 1000g = 1000/750 = 4/3.
3. Net SP/CP = (9/10) × (4/3) = 36/30 = 6/5.
4. Profit % = ((6 - 5) / 5) × 100 = 20%.

- [Practice more questions like this](https://testx.in/questions?q=dishonest+dealer)

### 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%.
**Step-by-Step Derivation**:
1. Assume Cost Price (CP) = ₹100.
2. Marked Price (MP) at 40% markup = ₹140.
3. Selling Price (SP) after 25% discount = 140 × (3/4) = ₹105.
4. Net Gain = ₹105 - ₹100 = 5%.

- [Practice more questions like this](https://testx.in/questions?q=marks+his+goods)
## Frequently Asked Questions

### Q: 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.

### Q: 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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