How to Solve Discount Problems

How to Solve Discount Problems

(For SSC, Bank, Railway Exams – Ace Your Exam with Confidence!)

Introduction

"Mastering discount problems can add 5–10 marks to your SSC/Bank/Railway exam score—because they appear in every quantitative section, and one small mistake can cost you the job! (Real-life impact: You’ll save money on shopping, calculate loans, and crack profit-loss questions faster.)

What You Need To Know First

Before diving in, ensure you understand: 1. Percentage basics – How to calculate 10% of 200 or increase/decrease a value by a percentage. 2. Profit & Loss – Terms like Marked Price (MP), Selling Price (SP), and Cost Price (CP). 3. Simple Interest – If discounts are combined with interest (e.g., "20% off + 5% cashback"), you’ll need this.

(If you’re shaky on any of these, pause and review them first—discounts build on these concepts!)

Key Vocabulary

Formulas To Know

1. Single Discount

Formula: Discount Amount = (Discount % × Marked Price) / 100 Selling Price (SP) = Marked Price (MP) – Discount Amount

Variables: - MP = Marked Price (original price) - Discount % = Percentage discount offered - SP = Selling Price (price after discount)

MEMORISE THIS – This is the foundation!

2. Successive Discounts (Two Discounts)

Formula: Final SP = MP × (1 – D₁/100) × (1 – D₂/100) (Where D₁ = first discount %, D₂ = second discount %)

Example: MP = ₹1000, D₁ = 10%, D₂ = 5% → SP = 1000 × (1 – 0.10) × (1 – 0.05) = 1000 × 0.9 × 0.95 = ₹855

MEMORISE THIS – Exams love testing this!

3. Equivalent Single Discount (for Successive Discounts)

Formula: Equivalent Discount % = 100 – [(100 – D₁) × (100 – D₂)] / 100

Example: D₁ = 10%, D₂ = 5% → Equivalent Discount = 100 – [(90 × 95) / 100] = 100 – 85.5 = 14.5%

MEMORISE THIS – Saves time in exams!

4. Cash Discount (Extra Discount on SP)

Formula: Final SP = SP × (1 – Cash Discount % / 100)

Example: SP = ₹900, Cash Discount = 2% → Final SP = 900 × (1 – 0.02) = ₹882

Given on exam sheet? Sometimes—check the question!

Step-by-Step Method

(Follow these steps for EVERY discount problem—no exceptions!)

1. Identify the Marked Price (MP).
2. Look for phrases like "labeled price," "tagged price," or "MRP."

3. If not given directly, assume MP = 100 (for percentage problems).

4. Note the Discount(s).

5. Single discount? → Use Discount Amount = (Discount % × MP) / 100.
6. Successive discounts? → Apply one after the other using SP = MP × (1 – D₁/100) × (1 – D₂/100).

7. Cash discount? → Apply it last, on the SP after all other discounts.

8. Calculate the Selling Price (SP).

9. For single discount: SP = MP – Discount Amount.
10. For successive discounts: Use the formula above.

11. For cash discount: Final SP = SP × (1 – Cash Discount %).

12. Check for Hidden Clues.

13. Words like "additional," "extra," or "cashback" mean another discount.

14. "Profit" or "loss" in the question? You may need to relate SP to CP.

15. Verify Your Answer.

16. Does the SP make sense? (Should be less than MP.)
17. Did you apply discounts in the correct order? (Successive discounts ≠ adding percentages!)

Worked Example Using the Steps

Question: A shirt is marked at ₹800. The shop offers a 15% discount, and an extra 5% cash discount if paid in cash. What is the final price if paid in cash?

Step-by-Step Solution:

1. Identify MP:
   MP = ₹800.

2. Note Discounts:

3. First discount = 15%

4. Extra cash discount = 5% (applied on SP after first discount).

5. Calculate First SP:
   Discount Amount = (15 × 800) / 100 = ₹120
   SP after first discount = 800 – 120 = ₹680

6. Apply Cash Discount:
   Cash Discount Amount = (5 × 680) / 100 = ₹34
   Final SP = 680 – 34 = ₹646

7. Verify:

8. ₹646 < ₹800 (correct, as discounts reduce price).
9. Order of discounts: 15% first, then 5% on ₹680 (correct).

Answer: ₹646

Worked Examples

Example 1 – Basic (Single Discount)

Question: A book is marked at ₹300. What is the selling price after a 20% discount?

Solution: 1. MP = ₹300 2. Discount % = 20% 3. Discount Amount = (20 × 300) / 100 = ₹60 4. SP = 300 – 60 = ₹240

What we did and why: - We used the single discount formula because only one discount was given. - Always calculate the discount amount first, then subtract from MP.

Example 2 – Medium (Successive Discounts)

Question: A jacket is marked at ₹2000. The shop offers a 10% discount, followed by an 8% discount. What is the final price?

Solution: 1. MP = ₹2000 2. First discount (D₁) = 10%
SP after first discount = 2000 × (1 – 0.10) = ₹1800 3. Second discount (D₂) = 8%
Final SP = 1800 × (1 – 0.08) = ₹1656

Alternative (Equivalent Discount): Equivalent Discount % = 100 – [(100 – 10) × (100 – 8)] / 100 = 100 – (90 × 92) / 100 = 100 – 82.8 = 17.2% Final SP = 2000 × (1 – 0.172) = ₹1656

What we did and why: - We applied discounts one after the other (not 10% + 8% = 18%!). - The equivalent discount method is faster but requires memorizing the formula.

Example 3 – Exam-Style (Disguised Problem)

Question: A retailer buys a fan for ₹1200 and marks it up by 25%. During a sale, he offers a 12% discount. What is the selling price? If he had given a 10% discount instead, how much more would he have earned?

Solution: Part 1: Selling Price with 12% Discount 1. CP = ₹1200 2. MP = CP + 25% of CP = 1200 + (0.25 × 1200) = ₹1500 3. Discount = 12% of MP = (12 × 1500) / 100 = ₹180 4. SP = 1500 – 180 = ₹1320

Part 2: Selling Price with 10% Discount 1. Discount = 10% of MP = (10 × 1500) / 100 = ₹150 2. SP = 1500 – 150 = ₹1350 3. Difference = 1350 – 1320 = ₹30

What we did and why: - We first found the Marked Price (MP) using the markup. - Then applied the discount to MP (not CP!). - The question asked for the difference, so we calculated both SPs.

Common Mistakes

Exam Traps

1-Minute Recap

(Spoken naturally, as if to a student the night before the exam.)

"Listen up—discount problems are easy marks if you follow these rules:

1. Find the Marked Price (MP) first. If it’s not given, assume MP = 100 for percentage problems.
2. Single discount? Just do (Discount % × MP) / 100 and subtract from MP.
3. Successive discounts? Never add percentages! Apply one after the other: MP × (1 – D₁/100) × (1 – D₂/100).
4. Cash discount? Apply it last, on the SP after all other discounts.
5. Check the order—discounts are applied in the sequence given in the question.
6. Verify—your final SP should always be less than MP.

Pro tip: If you see "equivalent discount," use 100 – [(100 – D₁) × (100 – D₂)] / 100. It’s faster!

Now go practice 3 problems—you’ve got this!