UPSC Prelims 2014·CSAT·Quantitative Aptitude·Arithmetic

A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden

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Last updated 23 May 2026, 3:31 pm IST
  1. Ahas increased by 20%
  2. Bhas increased by 12%Correct
  3. Chas increased by 8%
  4. Dis exactly the same as the old area.

Explanation

Let the original length of the rectangular garden be L and its original width be W. The original area of the garden = L * W. The length is increased by 40%. New length = L + 0.40L = 1.40L. The width is decreased by 20%. New width = W - 0.20W = 0.80W. The new area of the garden = (New length) * (New width) New area = (1.40L) * (0.80W) New area = (1.40 * 0.80) * (L * W) New area = 1.12 * (L * W) Since the original area was L * W, the new area is 1.12 times the original area. This means the new area is 112% of the original area. The percentage increase in area = (New Area - Original Area) / Original Area * 100 = (1.12 * Original Area - Original Area) / Original Area * 100 = (0.12 * Original Area) / Original Area * 100 = 0.12 * 100 = 12%. Therefore, the area of the new garden has increased by 12%. Option A is incorrect because the calculation shows a 12% increase, not 20%. Option B is correct as the new area is 1.12 times the old area, representing a 12% increase. Option C is incorrect as the increase is 12%, not 8%. Option D is incorrect as the new area is clearly greater than the old area (1.12 > 1). The final answer is B
Quantitative Aptitude: A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%.
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