UPSC Prelims 2005 Q99: Science & Technology – Quantitative Aptitude
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
Answer: (c) 120 m × 36 m
Explanation
Dividing a rectangular plot into square plots
| Step | Result |
|---|---|
| Original plot | 120 m x 36 m = 4320 sq m |
| 3 squares of side 36 m | Use 108 m of length; strip 12 m x 36 m left |
| Strip cut into squares | 3 squares of side 12 m: 36 / 12 = 3, nothing left over |
Option (c) fits both conditions: three 36 m squares leave a 12 m x 36 m strip, which then forms three 12 m squares with no waste. The area also equals 4320 sq m.
Answer: (c) 120 m x 36 m.
Why each option is right or wrong
- (a) Incorrect. 160 x 27 gives 4320 sq m, but 3 squares of 27 leave a 79 m strip that is not three equal squares.
- (b) Incorrect. 240 x 18 gives three 18 m squares and a 186 m strip, not three squares.
- (c) CORRECT. 120 x 36 satisfies both fencing conditions.
- (d) Incorrect. 135 x 32 does not give 4320 sq m.
Key point
Check area first, then test the square-cutting steps.
Remember
The plot measures 120 m by 36 m.
Common mistakes
- Checking only the area and ignoring the fencing steps.
- Cutting the squares along the wrong side.
- Not testing the left-over strip for squares.
Exam tip
Test each option: area, then 3 squares on the shorter side, then the left-over strip.
Sources
- NCERT Class VIII Mathematics — Mensuration
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Area)