UPSC Prelims 2004 · General Studies
Question 104: Basic Numeracy
A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 1 and 2.30 p.m.?
AnswerThe answer is (c).
The field's perimeter is 2 x (400 + 300) = 1,400 m. A walks at 3 km/h and B at 2.5 km/h, so A gains 0.5 km/h. They meet each time A gains a full lap, 1.4 km, which takes 1.4/0.5 = 2.8 hours: at 9:48 a.m. and 12:36 p.m., with a third meeting only at 3:24 p.m. By 1 p.m., and by 2:30 p.m., they have crossed twice.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) The first meeting comes at 9:48 a.m., so they cross at least once.
- (b) A second meeting follows at 12:36 p.m., before 1 p.m.
- (c) Correct: two meetings, at 9:48 a.m. and 12:36 p.m.
- (d) A third meeting would come only at 3:24 p.m., after both stated times.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2004, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.