1997 General Studies, all questions
UPSC Prelims 1997 · General Studies
Question 130: Basic Numeracy
A rectangular plot of lawn shown in the figure has dimensions x and y and is surrounded by a gravel pathway of width 2 m. What is the total area of the pathway?
a2x + 2y + 4
b2x + 2y + 8
c4x + 4y + 8
d4x + 4y + 16
AnswerThe answer is (d).
The path runs all round the lawn on four sides and is 2 m wide, so the outer rectangle measures (x + 4) by (y + 4). Area of the path = (x + 4)(y + 4) - xy = 4x + 4y + 16. Equivalently, the four side strips give 4x + 4y and the four corner squares of 2 m by 2 m give 16.
Why each option is right or wrong
- (a) 2x + 2y + 4 is the area for a path 1 m wide.
- (b) 2x + 2y + 8 counts only half the side strips.
- (c) 4x + 4y + 8 takes the corners as 8 instead of 16.
- (d) Right: 4x + 4y + 16.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1997, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.