UPSC Prelims 2005 Q97: Science & Technology – Quantitative Aptitude
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?
- (a) 14
- (b) 48
- (c) 96
- (d) 108
Answer: (d) 108
Explanation
Railway tickets with new stations
| Situation | One-way ticket types |
|---|---|
| Before: A, B and 10 stations = 12 stations | 12 x 11 = 132 |
| After: 12 + 4 = 16 stations | 16 x 15 = 240 |
| New tickets needed | 240 - 132 = 108 |
Each ordered pair of stations needs one ticket. With 16 stations there are 240 ordered pairs, against 132 earlier, so 108 new types of tickets are required.
Answer: (d) 108.
Why each option is right or wrong
- (a) Incorrect. 14 only counts the number of stations added and two ends.
- (b) Incorrect. 48 counts only tickets from the four new stations to the old ones.
- (c) Incorrect. 96 omits tickets among the four new stations.
- (d) CORRECT. 240 - 132 = 108 new ticket types.
Key point
n stations give n(n-1) one-way tickets.
Remember
12 stations give 132 tickets; 16 give 240; the new ones are 108.
Common mistakes
- Forgetting that A and B are also stations.
- Counting combinations instead of ordered pairs.
- Subtracting only the pairs of new with old stations.
Exam tip
One-way tickets mean order matters: use n(n-1).
Sources
- NCERT Class XI Mathematics — Permutations and Combinations
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Permutations and Combinations)