UPSC Prelims 2005 · General Studies
Question 99: Basic Numeracy
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?
AnswerThe answer is (c).
Let the sides be l (longer) and b (shorter), with l × b = 4320. Fencing across the longer side gives 3 squares of side b, leaving a strip b by (l − 3b). That strip is cut into 3 squares of side (l − 3b), so b = 3(l − 3b), which gives l = 10b/3. Then (10b/3) × b = 4320, so b² = 1296, b = 36 and l = 120.
Why each option is right or wrong
- (a) 160 and 27 do not satisfy l = 10b/3.
- (b) 240 and 18 do not satisfy l = 10b/3.
- (c) Correct: 120 = 10 × 36/3 and 120 × 36 = 4320.
- (d) 135 and 32 do not satisfy l = 10b/3.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2005, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.