Percentage increase and decrease

Introduction

Percentage change is a quick way to describe how much a quantity has grown or fallen compared with its original value. In SSC CHSL arithmetic, you must be able to find the changed value fast and accurately.

1. What percentage increase means

If a value increases by some percent, the increase is added to the original value.

Formula:

• Increase = Original value × Increase rate / 100
• New value = Original value + Increase

You can also write it directly as:

• New value = Original value × (100 + Increase rate) / 100

Worked example 1

A book costs 400. Its price increases by 15%.

Increase = 400 × 15 / 100 = 60

New price = 400 + 60 = 460

So the new price is 460.

2. What percentage decrease means

If a value decreases by some percent, the decrease is subtracted from the original value.

Formula:

• Decrease = Original value × Decrease rate / 100
• New value = Original value − Decrease

You can also write it directly as:

• New value = Original value × (100 − Decrease rate) / 100

Worked example 2

A chair costs 800. Its price is reduced by 12%.

Decrease = 800 × 12 / 100 = 96

New price = 800 − 96 = 704

So the new price is 704.

3. How to compare increase and decrease

• Use add for increase.
• Use subtract for decrease.
• Always calculate from the original value, not from the already changed value, unless the question clearly says there are two successive changes.

Worked example 3

A salary of 25,000 is increased by 8%.

Increase = 25,000 × 8 / 100 = 2,000

New salary = 25,000 + 2,000 = 27,000

Common mistakes

1. Using the changed value instead of the original value

• First find the change from the original amount.

2. Mixing up increase and decrease

• Increase means add, decrease means subtract.

3. Forgetting to divide by 100

• A percent always means “per 100”.

4. Applying the same percent to repeated stages carelessly

• If there are two changes, handle them step by step.

Practice

Try these questions.

1. A jacket costs 600. Its price increases by 10%. What is the new price?

• A. 650
• B. 660
• C. 680
• D. 700

2. A table costs 1,200. Its price decreases by 25%. What is the new price?

• A. 850
• B. 900
• C. 920
• D. 950

Practice answers

1. B. 660

• Increase = 600 × 10 / 100 = 60
• New price = 600 + 60 = 660

2. B. 900

• Decrease = 1,200 × 25 / 100 = 300
• New price = 1,200 − 300 = 900

Recap

• Percentage increase means original value + change.
• Percentage decrease means original value − change.
• Use original value to find the percent change.
• Direct formulas are:
• New value = Original × (100 + r) / 100 for increase
• New value = Original × (100 − r) / 100 for decrease

Analogy

The printed price is the original. A 10% rise on 600 adds 60, so the new price is 660. A 25% fall on 1200 takes away 300, so the new price is 900. The percent is taken from the original, then added or removed.

Quick reference

• Increase: new = original x (100 + r) / 100.
• Decrease: new = original x (100 - r) / 100.
• 600 increased by 10% becomes 660.
• 1200 decreased by 25% becomes 900.