UPSC Prelims 2014 CSAT Paper II · Q20 of 65 Basic Numeracy easy

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

  1. (a) has increased by 20%.
  2. (b) has increased by 12%. ✓ UPSC's answer
  3. (c) has increased by 8%.
  4. (d) is exactly the same as the old area.

Why the answer is (b)

• Let the original length be L and the original width be W, so the original area is L × W.

• The new length is 40% more than L, so it is 1.40L.

• The new width is 20% less than W, so it is 0.80W.

• The new area is 1.40L × 0.80W = 1.12LW.

• Since 1.12LW is 12% more than LW, the area has increased by 12%, so option (b) is correct.

Why the other options are wrong

(a) has increased by 20%.
The new area is 1.12 times the old area, not 1.20 times, so the increase is 12%, not 20%.
(c) has increased by 8%.
The product 1.40 × 0.80 equals 1.12, giving a 12% increase, not 8%.
(d) is exactly the same as the old area.
The new area is 1.12 times the old area, so it is not exactly the same as the old area.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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