# Profit, Loss and Discount — Formulas, Tricks and Solved Questions

Source: https://skills101.in/learn/aptitude/profit-loss-and-discount — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

Every shop buys something and sells it. Profit and loss questions just follow the money.

## 1. The three prices

![A shop buys at CP ₹800, puts a price tag MP ₹1000, gives a discount and sells at SP ₹900: discount ₹100, profit ₹100, profit 12.5%](https://skills101.in/learn-img/aptitude/profit-loss-flow.svg)

| Term | Meaning |
|---|---|
| **CP** — Cost Price | What the shopkeeper paid |
| **MP** — Marked Price (list price) | The price on the tag |
| **SP** — Selling Price | What the customer actually pays |

- **Profit** = SP − CP (when SP > CP)
- **Loss** = CP − SP (when CP > SP)
- **Discount** = MP − SP

> **The golden rule:** profit % and loss % are **always on CP**. Discount % is **always on MP**.

- Profit % = Profit ÷ CP × 100
- Discount % = Discount ÷ MP × 100

## 2. Use multipliers

- Sold at 20% profit → SP = CP × **1.2**
- Sold at 15% loss → SP = CP × **0.85**
- 10% discount → SP = MP × **0.9**

### Example 1
*A bicycle bought for ₹4,000 is sold at a 15% profit. Find the SP.*

SP = 4000 × 1.15 = **₹4,600**.

### Example 2
*By selling a watch for ₹1,140 a man loses 5%. At what price should he sell to gain 5%?*

CP × 0.95 = 1140 → CP = 1200. For 5% gain: 1200 × 1.05 = **₹1,260**.

## 3. Marked price and discount together

### Example 3
*A shopkeeper marks his goods 40% above cost and gives a 20% discount. What is his profit %?*

Take CP = 100. MP = 140. SP = 140 × 0.8 = 112. Profit = **12%**.

> **Trick: take CP = 100.** Most profit questions become one-line calculations.

## 4. Successive discounts

Two discounts of a% and b% are **not** a + b. Use the same rule as successive percentages:

> **Single equivalent discount = a + b − ab/100**

### Example 4
*Discounts of 20% and 10% one after another equal what single discount?*

20 + 10 − 200/100 = **28%** (not 30%).

## 5. Same SP, one profit and one loss

> If two items are sold at the **same SP**, one at x% profit and one at x% loss, there is **always a loss** of x²/100 %.

### Example 5
*Two phones are sold for ₹9,900 each. One at 10% profit, one at 10% loss. Net result?*

Loss = 10²/100 = **1% loss**. (Check: CPs are 9000 and 11000, total 20,000; SP total 19,800 → loss 200 = 1% ✓)

## 6. The dishonest shopkeeper (false weights)

### Example 6
*A shopkeeper claims to sell at cost price but uses a 900 g weight instead of 1 kg. What is his profit %?*

He gives 900 g but charges for 1000 g. He gains 100 g on 900 g.

> **Profit % = (error ÷ true weight given) × 100 = 100 ÷ 900 × 100 = 11.11%**

## 7. "Buy x, get y free"

### Example 7
*"Buy 4, get 1 free". What is the effective discount?*

The customer pays for 4 and gets 5. Discount = 1 ÷ 5 × 100 = **20%**.

## 8. CP of many vs SP of fewer

### Example 8
*The CP of 20 pens equals the SP of 16 pens. Find the profit %.*

Let each pen cost ₹1. CP of 16 pens = 16, SP of 16 pens = 20 (same as CP of 20). Profit = 4 on 16 → **25%**.

## Common mistakes

- Calculating profit % on SP. It is always on **CP**.
- Calculating discount % on CP. It is always on **MP**.
- Adding successive discounts (20% + 10% is 28%, not 30%).

## Quick recap

- Profit/loss % on CP; discount % on MP.
- Take CP = 100 and use multipliers.
- Successive discount: a + b − ab/100.
- Same SP, x% profit and x% loss → x²/100 % loss.
- False weight: error ÷ (true weight given) × 100.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/profit-loss-and-discount