How to Solve Percentage Problems

How to Solve Percentage Problems

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

Introduction

"Mastering percentages unlocks 5–10 marks in your SSC/Bank/Railway exam—enough to push you from ‘just passing’ to ‘top ranker.’ Whether it’s calculating discounts, interest rates, or profit margins, percentages are everywhere in real life and your exam. Let’s break them down step by step so you never lose a mark again."

What You Need To Know First

Before diving into percentages, ensure you’re comfortable with: 1. Fractions and decimals (e.g., 50% = ½ = 0.5). 2. Basic arithmetic (addition, subtraction, multiplication, division). 3. Ratio and proportion (e.g., if A:B = 2:3, then A = 2 parts, B = 3 parts).

Key Vocabulary

Formulas To Know

Step-by-Step Method

Step 1: Identify What’s Given and What’s Asked

• Read the question carefully.
• Underline the base (original number) and the percentage.
• Circle what you need to find (part, percentage, or base).

Step 2: Choose the Right Formula

• If you need the part (e.g., "What is 20% of 50?"), use: Part = (Percentage × Base) / 100
• If you need the percentage (e.g., "What % is 10 of 50?"), use: Percentage = (Part / Base) × 100
• If you need the base (e.g., "20% of what number is 10?"), rearrange: Base = (Part × 100) / Percentage

Step 3: Plug in the Numbers

• Substitute the values into the formula.
• Double-check units (e.g., ₹, kg, marks).

Step 4: Solve Step by Step

• Do multiplication/division first.
• Keep track of decimal places (e.g., 25% = 0.25).

Step 5: Verify Your Answer

• Ask: "Does this make sense?"
• Example: If 10% of a number is 50, the number should be larger than 50 (500).

Step 6: Handle Special Cases

• Successive percentages: Use the formula a + b + (a×b)/100.
• Profit/Loss: Use Increase/Decrease = (Change / Original) × 100.
• Discounts: Use Discount % = (MP – SP) / MP × 100.

Worked Examples

Example 1 – Basic

Question: What is 15% of 240?

Step 1: Identify given and asked. - Base = 240 - Percentage = 15% - Asked: Part (15% of 240)

Step 2: Choose formula. - Part = (Percentage × Base) / 100

Step 3: Plug in numbers. - Part = (15 × 240) / 100

Step 4: Solve. - 15 × 240 = 3600 - 3600 / 100 = 36

Step 5: Verify. - 10% of 240 = 24 - 5% of 240 = 12 - 24 + 12 = 36 ✔️

Answer: 36

What we did and why: We used the Part = (Percentage × Base) / 100 formula because we needed to find a portion of the base. Breaking 15% into 10% + 5% helped verify the answer quickly.

Example 2 – Medium

Question: A shirt costs ₹800 after a 20% discount. What was its marked price?

Step 1: Identify given and asked. - Selling Price (SP) = ₹800 - Discount = 20% - Asked: Marked Price (MP)

Step 2: Understand the relationship. - Discount = 20% of MP - SP = MP – Discount - So, SP = MP – (20% of MP) = 80% of MP

Step 3: Choose formula. - SP = (100% – Discount%) × MP - 800 = 80% × MP

Step 4: Rearrange to find MP. - MP = 800 / 0.80 - MP = 1000

Step 5: Verify. - 20% of 1000 = 200 - 1000 – 200 = 800 ✔️

Answer: ₹1000

What we did and why: We recognized that the selling price is the marked price minus the discount. Since 20% was discounted, 80% remained. We rearranged the formula to find the original price.

Example 3 – Exam-Style

Question: The price of a laptop increased by 10% in January and then decreased by 10% in February. What is the net percentage change?

Step 1: Identify given and asked. - First change = +10% - Second change = –10% - Asked: Net % change

Step 2: Use successive percentage formula. - Net % = a + b + (a×b)/100 - Here, a = +10, b = –10

Step 3: Plug in numbers. - Net % = 10 + (–10) + (10 × –10)/100 - Net % = 0 + (–100)/100 - Net % = –1%

Step 4: Interpret the result. - A –1% net change means the price decreased by 1% overall.

Step 5: Verify with numbers. - Assume original price = ₹100 - After 10% increase: 100 + 10 = ₹110 - After 10% decrease: 110 – 11 = ₹99 - Net change = 99 – 100 = –₹1 (–1%) ✔️

Answer: 1% decrease

What we did and why: We used the successive percentage formula because two changes were applied one after another. The key takeaway: A 10% increase followed by a 10% decrease does NOT bring you back to the original price!

Common Mistakes

Exam Traps

1-Minute Recap

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

"Okay, listen up—percentages are simple if you follow these rules:

1. Find the base first. That’s the number you’re taking the % of. If the question says ‘20% of 50,’ 50 is the base.
2. Use the right formula:
3. Part = (Percentage × Base) / 100
4. Percentage = (Part / Base) × 100
5. Base = (Part × 100) / Percentage
6. For increases/decreases, use (Change / Original) × 100.
7. For successive %, never add them directly! Use a + b + (a×b)/100.
8. Discounts? Selling Price = Marked Price × (100% – Discount%).
9. Double-check units—don’t mix up ₹, kg, or marks.
10. Verify your answer—does it make sense? If 10% of a number is 50, the number must be 500, not 5.

Most mistakes happen when you rush. Slow down, write every step, and you’ll get every mark. Now go practice 3–5 problems—you’ve got this!