Competitive Exams / CUET UG / Profit, Loss & Discount

Profit, Loss & Discount for CUET UG

Master profit and loss, discount, marked price, false weights, successive discount, and weighted transaction logic with original notes, solved examples, and a timed practice route.

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Overview

Why This Chapter Scores Well in CUET

This chapter repeats a small number of patterns: direct profit or loss, reverse CP or SP, marked price and discount, successive discount, equal gain-loss comparisons, false weights, and weighted stock-sale questions.

Once the base is identified correctly, most questions collapse quickly. That makes this one of the better chapters for speed plus accuracy gain.

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Section A

Notes & Concept Builder

Base first, factor next

1. Base Rule 2. Core Formulas 3. Multiplier Method 4. Successive Discount 5. Equal Gain and Equal Loss 6. False Weight 7. Weighted Transactions 8. Special Shortcuts

1. Base Rule

Profit and loss percentages are calculated on cost price. Discount percentage is calculated on marked price. Most mistakes in this chapter come from dividing by the wrong base.

\text{Profit\%}=\frac{\text{Profit}}{CP}\times100, \qquad \text{Discount\%}=\frac{\text{Discount}}{MP}\times100

2. Core Formulas

Keep these identities ready for direct and reverse questions.

SP=CP\times\frac{100+p}{100}, \qquad SP=CP\times\frac{100-l}{100}

SP=MP\times\frac{100-d}{100}, \qquad MP=SP\times\frac{100}{100-d}

3. Multiplier Method

Convert each percentage into a factor. A 20% gain means 1.20, a 10% loss means 0.90, and a 15% discount means 0.85. This is the fastest way to handle chained changes.

4. Successive Discount

Successive discounts multiply. They do not add.

\text{Net discount}=a+b-\frac{ab}{100}

For more than two discounts, multiply the unpaid parts directly.

5. Equal Gain and Equal Loss

If two articles have equal cost price or equal selling price and one is sold at x% gain while the other is sold at x% loss, the overall result is always a loss.

\text{Overall loss\%}=\frac{x^2}{100}

6. False Weight

If a trader charges for 1 kg but gives only $w$ grams while claiming to sell at cost price, the shortage itself creates profit.

\text{Gain\%}=\frac{1000-w}{w}\times100

7. Weighted Transactions

If different shares of stock are sold at different gains or losses, use weighted averages. Do not take a simple average unless the shares are equal.

\text{Overall\%}=\sum (\text{share}\times\text{rate})

8. Special Shortcuts

\text{If CP of a articles = SP of b articles, Profit\%}=\frac{a-b}{b}\times100

\text{If profit amount = loss amount, } CP=\frac{SP_1+SP_2}{2}

Solved Practice

Solved Examples

Try mentally first

Example 1: A notebook set is bought for Rs 240 and sold for Rs 282. Find the profit percentage.

Profit $=42$ .

Profit\% $=\frac{42}{240}\times100=17.5\%$ .

Example 2: A lamp is sold for Rs 504 after being bought for Rs 560. Find the loss percentage.

Loss $=56$ .

Loss\% $=\frac{56}{560}\times100=10\%$ .

Example 3: A bag costs Rs 750 and is sold at 24% profit. Find the selling price.

$SP=750\times1.24=930$ .

Example 4: A speaker is sold for Rs 1,380 at 15% gain. Find the cost price.

$CP=1380\times\frac{100}{115}=1200$ .

Example 5: A cycle is sold for Rs 2,160 at 10% loss. Find the cost price.

$CP=2160\times\frac{100}{90}=2400$ .

Example 6: Two shirts have equal cost price. One is sold at 18% gain and the other at 18% loss. Find the overall result.

Loss $=\frac{18^2}{100}=3.24\%$ .

Example 7: CP of 15 pens equals SP of 12 pens. Find the profit percentage.

Profit\% $=\frac{15-12}{12}\times100=25\%$ .

Example 8: A trader gives only 960 g for 1 kg while selling at cost price. Find the gain percentage.

Gain\% $=\frac{40}{960}\times100=4.166\ldots\%$ .

Example 9: A dress marked Rs 2,400 is sold at 15% discount. Find the selling price.

$SP=2400\times0.85=2040$ .

Example 10: An article is sold for Rs 1,530 after a 10% discount. Find the marked price.

$MP=1530\times\frac{100}{90}=1700$ .

Example 11: Find the equivalent single discount of 20% and 15%.

Net discount $=20+15-3=32\%$ .

Example 12: A store gives 12% discount and still wants 25% gain. Find markup percentage.

Take $CP=100$ .

Needed $SP=125$ .

$MP=\frac{125}{0.88}=142.045\ldots$ so markup is about 42.05%.

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Section B

The Test Zone

The practice route splits this chapter into four focused sessions: core profit and loss, discount and marked price, false weights and mixtures, and advanced mixed cases. Then the full mock blends all 40 questions into one timed drill.

Sectional Tests

4 focused sessions on direct formulas, discounts, false weights, and mixed transactions.

Open Sectional Tests

Full Mixed Mock

40 questions with a 60-second timer per question so we practice recognition speed as well as arithmetic accuracy.

Start Mixed Mock

Finished this topic?

Keep the practice loop moving

Move straight from chapter-wise questions into a subject test, then loop back into weaker areas instead of ending the session here.

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