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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: If the length and breadth of a rectangle is decreased by 8% and 5% respectively, by what percentage will the area of the rectangle be decreased? Quantity B: If the side of a square is decreased by 6%, by what percentage will the area of the square be decreased?

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: If the length and breadth of a rectangle is decreased by 8% and 5% respectively, by what percentage will the area of the rectangle be decreased? Quantity B: If the side of a square is decreased by 6%, by what percentage will the area of the square be decreased? Correct Answer Quantity A > Quantity B

Solving for Quantity A:

Let the initial length and breadth of the rectangle be ‘l’ and ‘b’ units respectively

New length = (100 - 8)% of l = 92% of l = 0.92l

New breadth = (100 - 5)% of b = 95% of b = 0.95b

New area = 0.92l × 0.95b = 0.874(lb) = 87.4% of initial area

Hence, the area is decreased by = 100 - 87.4 = 12.6%

⇒ Quantity A = 12.6%

Solving for Quantity B:

Let the initial side of the square be ‘s’ units

New side = (100 - 6)% of s = 94% of s = 0.94s

New area = 0.94s × 0.94s = 0.8836s2 = 88.36% of initial area

Hence, the area is decreased by = 100 - 88.36 = 11.64%

⇒ Quantity B = 11.64%

∴ Quantity A > Quantity B

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