Multiple choice

The plinth of a house has an area of 200 square metres. It is rectangular in shape and its length and breadth are in the ratio 2 : 1. The owner of the house extends the terrace by 1 m on each side. What is the percentage of area that has increased in the terrace relative to the plinth?

  1. 40%

  2. 32%

  3. 20%

  4. 15.5%
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B Correct answer
Explanation

Area = 200, ratio 2:1. 2x * x = 200 => x^2 = 100 => x = 10. Dimensions are 20m and 10m. New dimensions after 1m extension on each side: (20+2) and (10+2) = 22m and 12m. New area = 22 * 12 = 264. Increase = 64. Percentage increase = (64/200) * 100 = 32%.

AI explanation

Let the length and breadth of the plinth be 2x and x, so its area (2x^2) equals 200 square metres, making x equal to 10. The original dimensions are 20 m by 10 m, and extending the terrace by 1 m on each side adds 2 m to both the length and breadth, creating a new rectangle of 22 m by 12 m. The new area becomes 264 square metres, which is an increase of 64 square metres over the original plinth. Calculating the percentage increase using the formula (increase / original area) * 100 gives (64 / 200) * 100, resulting in a 32% increase.

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