A rectangle has length 40 cm, breadth 20 cm. Length is increased by 25% and breadth is increased by 20%. What will the the percent change in area?

Question: A rectangle has length 40 cm, breadth 20 cm. Length is increased by 25% and breadth is increased by 20%. What will the the percent change in area ?

• 10%
• 25%
• 50% 
• 75% 

Answer: 

• $A$ = Percentage change in length = 25%
• $B$ = Percentage change in breadth = 20%

Applying  'AB METHOD' : ✌️

$$\text{Percentage Change in Area} = 25 + 20 + \frac{25 \times 20}{100}$$ $$= 25 + 20 + \frac{500}{100}$$ $$= 25 + 20 + 5$$ $$= 50\%$$

'_' The percentage increase in area is 50%

Additional Method (In Detail Solution):-

Given:

• Original length = 40 cm
• Original breadth = 20 cm
• Original area = $40 \times 20 = 800$ cm²

New dimensions:

• New length = $40 + 25\%$ of 40 $$= 40 + \frac{25}{100} \times 40 = 40 + 10 = 50 \text{ cm}$$
• New breadth = $20 + 20\%$ of 20 $$= 20 + \frac{20}{100} \times 20 = 20 + 4 = 24 \text{ cm}$$

New area:

$$= 50 \times 24 = 1200 \text{ cm}^2$$

Percentage change in area:

$$\frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \times 100$$ $$= \frac{1200 - 800}{800} \times 100$$ $$= \frac{400}{800} \times 100$$ $$= 50\%$$

'_'  The percentage increase in area is 50%.

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