Question

# Find the percentage change in the area of a rectangle if its length is increased by 25% and its breath is decreased by 20%. यदि एक आयत की लंबाई 25% बढ़ती है और उसकी चौड़ाई 20% घटती है, तो आयत के क्षेत्रफल में हुए परिवर्तन का प्रतिशत ज्ञात करें।

A
+6.7%
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B
-1.12%
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C
+2.14%
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D
No change

कोई परिवर्तन नहीं
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Solution

## The correct option is D. No changeकोई परिवर्तन नहींLet the length, breadth of the rectangle be L and B respectively. Original area =L×BNew length =L+25% of L=L+L×25100=5L4New breath =B−20% of B=B−B×20100=4B5 New area 5L4×4B5=LBChange in area =LB−LB=0Thus, there will be no change in the area of the rectangle. माना की आयत की लंबाई, चौड़ाई क्रमश: L और B है।नया लम्बाई =L+25% of L=L+L×25100=5L4नया चौड़ाई =B−20% of B=B−B×20100=4B5 ∴ मूल क्षेत्रफल =L×B नया क्षेत्रफल =5L4×4B5=LBक्षेत्रफल में परिवर्तन =LB−LB=0 इसलिए आयत के क्षेत्रफल में कोई परिवर्तन नहीं होगा।

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