UPSC Prelims 2003 Q120: Science & Technology – Quantitative Aptitude
Three bells toll at intervals of 9, 12 and 15 minutes respectively. All three begin to toll at 8
a.m. At what time will they first toll together again?
- (a) 8.45 a.m.
- (b) 10.30 a.m.
- (c) 11.00 a.m.
- (d) 1.30 p.m.
Answer: (c) 11.00 a.m.
Explanation
Three bells tolling together
| Quantity | Value |
|---|---|
| Intervals | 9, 12 and 15 minutes |
| LCM of 9, 12, 15 | 180 minutes |
| First common toll again | 8:00 a.m. + 3 hours = 11:00 a.m. |
The three bells toll together again after the LCM of 9, 12 and 15, which is 180 minutes, so at 11:00 a.m.
Answer: (c) 11.00 a.m.
Why each option is right or wrong
- (a) Incorrect. 8:45 a.m. is after 45 minutes, not a common multiple.
- (b) Incorrect. 10:30 a.m. is after 150 minutes, not a common multiple.
- (c) CORRECT. LCM = 180 minutes = 3 hours.
- (d) Incorrect. 1:30 p.m. is after 330 minutes, not the first common time.
Key point
Bells tolling together again: use the LCM of the intervals.
Remember
The bells toll together again after 180 minutes, at 11 a.m.
Common mistakes
- Using the HCF (3) instead of the LCM.
- Adding the three intervals together.
- Making an error in the LCM of 9, 12 and 15.
Exam tip
LCM of 9, 12 and 15 = 2^2 x 3^2 x 5 = 180.
Sources
- NCERT Class X Mathematics — Real Numbers
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (H.C.F. and L.C.M. of Numbers)