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Question

If the length of a rectangle is increased by 40% and its breadth is decreased by 60% then what will be the change in its area?

यदि आयत की लंबाई में 40% की वृद्धि और इसकी चौड़ाई में 60% की कमी कर दी जाए तो इसके क्षेत्रफल में क्या परिवर्तन होगा?

A
Increase by 44%

44% वृद्धि
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B
Decrease by 44%

44 % ह्रास
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C
Increase by 56%

56% वृद्धि
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D
Decrease by 56%

56 % ह्रास
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Solution

The correct option is B Decrease by 44%

44 % ह्रास
We know that the area of rectangle is Length X Breadth.
Let L and B be the length and breadth of the rectangle. So the area of original rectangle, A = L × B
Now, the area of new rectangle = 1.4 L × 0.4 B = (1.4 × 0.4) (L × B) = 0.56 A
Thus, the new area is 56% of the original rectangle, i.e. there is decrease of 44% in the area.

हम जानते हैं कि आयत का क्षेत्रफल लंबाई × चौड़ाई होता है।
माना कि L और B क्रमशः आयत की लंबाई और चौड़ाई हैं। इसलिए वास्तविक आयत का क्षेत्रफल, A = L × B
अब, नए आयत का क्षेत्रफल = 1.4L × 0.4 B = (1.4 × 0.4) (L × B) = 0.56 A
इस प्रकार, नया क्षेत्रफल वास्तविक क्षेत्रफल का 56% है, अर्थात् क्षेत्रफल में 44% की कमी हो रही है।

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