UPSC Prelims 2003 · General Studies
Question 44: Basic Numeracy
A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is
AnswerThe answer is (a).
For equal distances, the average speed is total distance over total time, which is the harmonic mean of the speeds. Take each third as d. Time = d/10 + d/20 + d/60 = d(6 + 3 + 1)/60 = d/6. Total distance is 3d, so the average speed = 3d / (d/6) = 18 km/hr. The simple average (30) is wrong because the car spends more time at the slow speed.
Why each option is right or wrong
- (a) Correct: 3d divided by d/6 gives 18 km/hr.
- (b) 24 is not what total distance over total time gives.
- (c) 30 is the simple average of the speeds, which ignores the time spent at each speed.
- (d) 36 is not what total distance over total time gives.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2003, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.