UPSC Prelims 2010 · General Studies
Question 101: Basic Numeracy
Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5·5 and 8 kmph respectively. When will they meet at the starting point for the first time ?
AnswerThe answer is (c).
The men take 11/4 = 2.75 hours, 11/5.5 = 2 hours and 11/8 = 1.375 hours to complete one lap. They are together at the start only at a time that is a whole number of laps for each. At time t, the laps run are 4t/11, t/2 and 8t/11. For t/2 to be a whole number t must be even, and for 4t/11 and 8t/11 to be whole numbers t must be a multiple of 11. The smallest such t is 22 hours (8, 11 and 16 laps).
Why each option is right or wrong
- (a) At 11 hours the second man has run 5.5 laps, so he is not at the start.
- (b) 21 hours is not a multiple of 11 or of 2.
- (c) Right: at 22 hours the three have run 8, 11 and 16 whole laps.
- (d) At 33 hours the second man has run 16.5 laps, so he is not at the start.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.