1.

If the length of the rectangle is increased by 40% and breadth decreases by 50% and this whole process is repeated again then what will be the percentage change in area?1). 10%2). 90%3). 50%4). 51%

Answer»

TRICK:

If length is increased by 40% and breadth is decreased by 50% then % change WOULD be 30%. Now again the PROCESS is repeated and now %change would be 21%. Overall percentage change = 51%

Detailed SOLUTION:

Let the initial length and breadth be x and y respectively

Area = xy

Now length is increased by 40% and breadth is decreased by 50%

⇒ New length = x + (40% of x) = (140/100)x

⇒ New breadth = y – (50% of y) = (50/100)y

Now after repeating the same process

⇒ New length = (140/100)x + {40% of (140/100)x}

⇒ (140/100)x + (56/100)x = (196/100)x

⇒ New breadth = (50/100)y – {50% of (50/100)y}

⇒ (50/100)y – (25/100)y = (25/100)y

⇒ New Area = {(196/100)x} × {(25/100)y} = (49/100)xy

∴ Percentage change in area = [{xy – (49/100)xy}/xy] × 100 = 51%


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