If the length of a rectangle is increased by 20% and its bread... | Mathematics MCQ | Examoogle

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MathematicsGeometry

If the length of a rectangle is increased by 20% and its breadth is decreased by 10%, what is the percentage change in its area?

8% increase

10% increase

5% increase

12% increase

Correct Answer

📐 MA • Math Successive FormulaMathematicsGeometry

Option A

8% increase

Quick Summary:

Apply the successive percentage change formula directly: $x + y + \frac{xy}{100}$ to compute the net area change within seconds.

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📐MAMath SolutionSuccessive Formula

📋 Given

Length of the rectangle is increased by 20% and breadth is decreased by 10%.

🔢 Formula Used

Net Change=x+y+x×y100\text{Net Change} = x + y + \frac{x \times y}{100}Net Change=x+y+100x×y​

⚡ Exam Hall Shortcut / Speed Trick

Apply the successive percentage change formula directly: $x + y + \frac{xy}{100}$ to compute the net area change within seconds.

⚠️ Common Student Trap / Pitfall

Students often make the mistake of simply subtracting the decrease from the increase ( $20\% - 10\% = 10\%$ ), ignoring the multiplicative effect of dimensions.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Percentage Changes

Assign the percentage changes in length and breadth to variables $x$ and $y$ .

x=+20%,y=−10%x = +20\%, \quad y = -10\%x=+20%,y=−10%

Apply Successive Percentage Formula

Use the standard formula for the combined percentage change of two successive dimensions.

Net Change=x+y+x×y100\text{Net Change} = x + y + \frac{x \times y}{100}Net Change=x+y+100x×y​

Substitute and Calculate

Substitute $x = 20$ and $y = -10$ into the equation and simplify.

20−10+20×(−10)100=10−2=8%20 - 10 + \frac{20 \times (-10)}{100} = 10^{-2} = 8\%20−10+10020×(−10)​=10−2=8%

Final Conclusion

A positive final value of $8\%$ indicates an increase in the total area, matching option A.

Area increases by 8%\text{Area increases by } 8\%Area increases by 8%

✅

A is correct because the calculated net percentage change in area is an 8% increase.

Core Concepts Used

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Successive Percentage Percentage Change Area of Rectangle

💡 EXAM TIP

The successive percentage formula is universally applicable to problems involving successive discounts, profit and loss, and population growth.

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