UPSC Prelims 2002 · General Studies
Question 91: Basic Numeracy
Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?
AnswerThe answer is (c).
Let the second lady walk at v km/h and the first at v + 2. Their times over 24 km are 24/v and 24/(v + 2), and the difference is 1 hour: 24/v - 24/(v + 2) = 1. So 48 = v(v + 2), i.e. v squared + 2v - 48 = 0, giving v = 6. The speeds are 8 and 6 km/h. Check: 24/6 = 4 h and 24/8 = 3 h, a gap of 1 hour.
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) 5 and 3 give times of 4.8 h and 8 h, a gap of 3.2 h.
- (b) 7 and 5 give times of about 3.4 h and 4.8 h, a gap of about 1.4 h.
- (c) Right: 8 and 6 give 3 h and 4 h, a gap of 1 h.
- (d) 16 and 14 give about 1.5 h and 1.7 h, a gap of about 0.2 h.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2002, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.