How to Solve: CUET Quant – Profit, Loss, and Discount

How to Solve: CUET Quant – Profit, Loss, and Discount

Introduction

"Imagine you’re running a small business—every rupee you save or lose affects your bottom line. CUET tests this exact skill: calculating profit, loss, and discounts under pressure. Master this, and you’ll solve 5-7 questions in under 10 minutes—guaranteed."

What You Need To Know First

1. Percentage Basics – How to calculate % increase/decrease (e.g., 20% of ₹500 = ₹100).
2. Cost Price (CP) vs. Selling Price (SP) – CP is what you pay; SP is what you sell for.
3. Basic Arithmetic – Addition, subtraction, multiplication, and division of decimals.

If you’re shaky on these, pause and review them first.

Key Vocabulary

Formulas To Know

(All must be memorized—CUET does not provide these!)

1. Profit Formula
   [
   \text{Profit} = \text{SP} - \text{CP}
   ]
   [
   \text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100
   ]

2. Loss Formula
   [
   \text{Loss} = \text{CP} - \text{SP}
   ]
   [
   \text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100
   ]

3. Selling Price (SP) from Profit/Loss %

4. If Profit:
   [
   \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)
   ]

5. If Loss:
   [
   \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right)
   ]

6. Discount Formula
   [
   \text{Discount} = \text{MP} - \text{SP}
   ]
   [
   \text{Discount \%} = \left( \frac{\text{Discount}}{\text{MP}} \right) \times 100
   ]
   [
   \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount \%}}{100}\right)
   ]

7. Successive Discounts

8. For two discounts (e.g., 10% + 20%):
   [
   \text{Total Discount} = 100 - \left[(100 - 10) \times \left(1 - \frac{20}{100}\right)\right]
   ]
   [
   \text{SP} = \text{MP} \times \left(1 - \frac{\text{First Discount}}{100}\right) \times \left(1 - \frac{\text{Second Discount}}{100}\right)
   ]

Step-by-Step Method

(Follow these steps for every profit/loss/discount problem.)

1. Identify the Given Values
2. Write down: CP, SP, MP, Profit %, Loss %, Discount %.

3. Circle what you need to find.

4. Choose the Right Formula

5. Profit/Loss? → Use Profit/Loss % formulas.
6. Discount? → Use Discount % or SP = MP × (1 – Discount %).

7. Successive discounts? → Apply one after the other.

8. Plug in the Numbers

9. Substitute values into the formula.

10. Double-check units (e.g., ₹ vs. %, CP vs. MP).

11. Solve Step-by-Step

12. Break calculations into small parts (e.g., first find 10% of CP, then add to CP).

13. Avoid mental math—write every step.

14. Verify the Answer

15. Does it make sense? (e.g., SP > CP → Profit, not loss.)
16. Recalculate if unsure.

Worked Example (Using Steps Above)

Problem: A shopkeeper buys a shirt for ₹800 and sells it at a 15% profit. What is the selling price?

Solution: 1. Given:
- CP = ₹800
- Profit % = 15%
- Find: SP

1. Formula:
   [
   \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)
   ]

2. Plug in:
   [
   \text{SP} = 800 \times \left(1 + \frac{15}{100}\right) = 800 \times 1.15
   ]

3. Solve:
   [
   800 \times 1.15 = 920
   ]

4. Verify:

5. Profit = ₹920 – ₹800 = ₹120.
6. Profit % = (120/800) × 100 = 15% ✔️

Answer: ₹920

Worked Examples

Example 1 – Basic (Profit %)

Problem: A book is bought for ₹250 and sold for ₹300. Find the profit percentage.

Solution: 1. CP = ₹250, SP = ₹300 2. Profit = SP – CP = ₹300 – ₹250 = ₹50 3. Profit % = (Profit/CP) × 100 = (50/250) × 100 = 20%

Answer: 20%

What we did and why: - Found profit amount first (SP – CP). - Used the profit % formula to express it as a percentage of CP.

Example 2 – Medium (Discount + Profit)

Problem: A jacket is marked at ₹2,000. The shop offers a 10% discount but still makes a 20% profit. Find the cost price.

Solution: 1. MP = ₹2,000, Discount = 10% 2. SP = MP × (1 – Discount %) = 2000 × 0.90 = ₹1,800 3. Profit = 20%, so:
[
\text{SP} = \text{CP} \times (1 + \text{Profit \%}) \Rightarrow 1800 = \text{CP} \times 1.20
] 4. CP = 1800 / 1.20 = ₹1,500

Answer: ₹1,500

What we did and why: - First found SP after discount. - Then used SP to find CP, knowing the profit %.

Example 3 – Exam Style (Successive Discounts)

Problem: A laptop is marked at ₹50,000. The shop offers discounts of 10% and then 5%. What is the final selling price?

Solution: 1. MP = ₹50,000 2. First discount (10%):
[
\text{SP}_1 = 50,000 \times (1 - 0.10) = ₹45,000
] 3. Second discount (5% on ₹45,000):
[
\text{SP}_2 = 45,000 \times (1 - 0.05) = ₹42,750
]

Answer: ₹42,750

What we did and why: - Applied discounts one after the other (not 15% total!). - Multiplied the remaining amount by (1 – discount %) each time.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, let’s lock this in. Profit, loss, and discount problems are all about three things: CP, SP, and MP. Here’s the cheat sheet:

1. Profit/Loss: Always compare SP to CP. Profit % = (Profit/CP) × 100. Loss % = (Loss/CP) × 100.
2. Discount: Always on MP. SP = MP × (1 – Discount %). Never use CP here!
3. Successive Discounts: Apply one after the other. 10% off, then 20% off ≠ 30% off.
4. Watch for traps: Discounts on MP, not CP. Profit % on CP, not SP.

Tonight, do 5 problems—two profit, two discount, one successive discount. Write every step. You’ve got this!