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UPSC 2005: A big rectangular plot of area 4320 m² is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot?
(a)160 m × 27 m
(b)240 m × 18 m
(c)120 m × 36 m
(d)135 m × 32 m
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Not attemptedCorrect Answer: (c) 120 m × 36 m
Let the rectangle be L × W (L > W). Three squares of side W use 3W length, leaving (L – 3W) by W. For the leftover strip to be tessellated into three smaller squares, the strip length must divide the width exactly, i.e. W = 3 (L – 3W). Solving with area LW = 4320 yields W = 36 m and L = 120 m, giving 3 big squares (36 m) and 3 small squares (12 m). Only option (c) 120 m × 36 m satisfies both the arithmetic and the area of 4320 m²; the other options fail either the area condition or the divisibility condition.
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Frequently Asked Questions
What is the correct answer to this UPSC 2005 Science & Technology question?▼
The correct answer is option (c): 120 m × 36 m. Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Quantitative Aptitude question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 2005, GS Paper 1, as Question 99. It falls under Science & Technology > Quantitative Aptitude.
What is the difficulty level of this UPSC question?▼
This question is rated "difficult". It is a challenging question that demands deep subject knowledge and analytical thinking.
How many UPSC Prelims questions have been asked from Quantitative Aptitude?▼
UPSC has asked 178 questions from Quantitative Aptitude (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.