Height and breadth of a rectangle are 40 cm and 20 cm respectively. If the length increases by 25%, by what percent breadth must be decreased to maintain the same area?

Questions : Height and breadth of a rectangle are 40 cm and 20 cm respectively. If the length increases by 25%, by what percent breadth must be decreased to maintain the same area?

Answer:  

 

Given:

• Original length = 40 cm
• Original breadth = 20 cm
• Original area = $40 \times 20 = 800$ cm²
• New length = $40 + 25\%$ of 40 $$= 40 + \frac{25}{100} \times 40 = 40 + 10 = 50 \text{ cm}$$
• New breadth = $x$ cm (to be found)
• New area must remain 800 cm²

Using the area equation:

$$50 \times x = 800$$

Solving for $x$:

$$x = \frac{800}{50} = 16 \text{ cm}$$

Percentage decrease in breadth:

$$\frac{\text{Original breadth} - \text{New breadth}}{\text{Original breadth}} \times 100$$ $$= \frac{20 - 16}{20} \times 100$$ $$= \frac{4}{20} \times 100 = 20\%$$

Final Answer:

Breadth must be decreased by 20%.

Short Cut 

You can use the shortcut formula for percentage decrease:

$$\text{Percentage Decrease} = \frac{\text{Increase in Length} \times 100}{\text{Increase in Length} + 100}$$

Given:

• Length increases by 25%

Applying the formula:

$$\text{Percentage Decrease} = \frac{25 \times 100}{25 + 100}$$ $$= \frac{2500}{125} = 20\%$$

Final Answer:

Breadth must be decreased by 20%.

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