UPSC Prelims 2005 · General Studies
Question 97: Basic Numeracy
On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?
AnswerThe answer is (d).
The route has 10 stations plus A and B, 12 in all. A one-way ticket is needed for each ordered pair of stations, so 12 × 11 = 132 types. With 4 new stations there are 16 stations: 16 × 15 = 240 types. New ticket types required: 240 − 132 = 108.
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) 14 is just 10 stations plus 4 new ones, not a count of ticket types.
- (b) 48 is not what the count gives.
- (c) 96 is not what the count gives.
- (d) Correct: 240 − 132 = 108.
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.