Percentage – MBA CUET PG – Notes & Practice Questions

Basic Definition

• Percentage: A fraction with denominator 100.

$$x\% = \frac{x}{100}$$

​

• Converting % → fraction quickly:

  • 10% = 1/10

  • 20% = 1/5

  • 25% = 1/4

  • 12.5% = 1/8

  • 16⅔% = 1/6

  • 33⅓% = 1/3

  • 50% = 1/2

  • 66⅔% = 2/3

  • 75% = 3/4

  • 80% = 4/5

These are must-memorize for speed.

Percentage Change

Increase

If a quantity increases by x%:

$$\text{New Value} = \text{Old Value} \times \left(1 + \frac{x}{100}\right)$$

Decrease

If decrease is x%:

$$\text{New Value}=\text{Old Value}\times (1-\frac{x}{100})$$

Reverse Percentage

If A becomes B after x% increase/decrease:

$$\text{Original Value} = \frac{\text{New Value}}{1 \pm \frac{x}{100}}$$

​

Examples:

• After 25% increase → divide by 1.25

• After 20% decrease → divide by 0.8

Successive Percentage Changes

If two percentage changes occur: a% and b%

$$\text{Net Change\%} = a + b + \frac{ab}{100}$$

​

If one is + and other is −, carry sign accordingly:

$$\text{Net Change\%} = a – b – \frac{ab}{100}$$

​

Special case:

• +20% then −20% → net = -4% (always loss)

Ratio ↔ Percentage Conversion:

If ratio is a:b

Percentage of first:

$$\frac{a}{a+b} \times 100$$

Percentage increase from a to b:

$$\frac{b-a}{a} \times 100$$

Population Growth/Decay Formula (Repeated % Change)

For growth:

$$P_n = P_0 (1 + \frac{r}{100})^n$$

For decay:

$$P_n = P_0 (1 – \frac{r}{100})^n$$

Value vs. Percentage Comparison Shortcut

When comparing % increase between two quantities:

$$\text{Difference\%} = \frac{\text{Difference}}{\text{Base Value}} \times 100$$

Always check the base — most mistakes in exams arise from wrong base.

Percentage Points

Useful in DI:

• Increase from 20% to 25% = 5 percentage points, not 5%.

• 5 percentage points = actual increase =

$$\frac{25-20}{20} \times 100 = 25\%$$

Short Tricks

x% of y = y% of x

Shortcut useful in quick calculation.

Example:

• 12.5% of 48 = 48% of 12.5

To find what % A is of B

$$\frac{A}{B} \times 100$$

If A is x% more than B

Then B is less than A by:

$$\frac{x}{100+x} \times 100\%$$

Example: A = 25% more than B
→ B is

$\frac{25}{125} = 20\%$

 less than A.

If A is x% less than B

Then B is more than A by:

$$\frac{x}{100-x} \times 100\%$$

Converting Fraction ↔ Percentage Fast

• 1/8 = 12.5%

• 1/6 = 16.66%

• 1/5 = 20%

• 1/4 = 25%

• 1/3 = 33.33%

• 2/3 = 66.66%

• 3/4 = 75%

Good for DI + arithmetic.

Profit-Loss-Percentage Links

Although not PL topic, percentage shortcuts help:

Profit% =

$$\frac{SP – CP}{CP} \times 100$$

Loss% =

$$\frac{CP – SP}{CP} \times 100$$

Selling price = CP × (1 ± % change)

Exam-Oriented Replacements

Percentage increase ≠ increase in percentage points

Always differentiate.

If quantity increases by x% and price decreases by y%:

$$\text{Net Effect} = x – y – \frac{xy}{100}$$

Often used in consumption problems.

Percentage Error (Measurement)

If measured value = M, actual value = A:

$$\text{Error\%} = \frac{M – A}{A} \times 100$$

If instrument gives 5% extra reading → multiply by 0.95 to get true value.

Exam-Fast Methods

Mini Tricks:

• Increase by 10% → multiply by 1.1

• Decrease by 10% → multiply by 0.9

• +20% then −20% always = −4%

• 40% of 120 = 120 of 40 trick

• If value becomes P% of itself, percentage change = P − 100

Examples:

• Becomes 80% of earlier → 20% decrease

• Becomes 150% → 50% increase

Practice Questions

1. A number is increased by 20% and then decreased by 20%. What is the net percentage change?
A) 0%
B) 2% decrease
C) 4% decrease
D) 4% increase

2. A value becomes 135% of itself. What is the percentage increase?
A) 25%
B) 30%
C) 35%
D) 40%

3. A’s salary is 25% more than B’s salary. B’s salary is what percent less than A’s?
A) 15%
B) 18%
C) 20%
D) 25%

4. A number is first increased by 30% and then increased again by 20%. Find total % increase.
A) 50%
B) 56%
C) 60%
D) 66%

5. A number is decreased by 40% and then increased by 40%. Net effect = ?
A) 0%
B) 4% increase
C) 4% decrease
D) 16% decrease