In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart ?
- (a) 40 m
- (b) 50 m
- (c) 75 m
- (d) 150 m ✓ UPSC's answer
Why the answer is (d)
• The bucket is at the start (0 m), and the first apple is 5 m away, with subsequent apples 3 m apart.
• The positions of the 6 apples are: 5 m, 8 m, 11 m, 14 m, 17 m, and 20 m from the start.
• Since the competitor must return to the bucket after each apple, the distance for each trip is twice the position of that apple.
• The total distance is the sum of round trips: 2*(5 + 8 + 11 + 14 + 17 + 20).
• The sum of the positions is 75 m, so the total distance is 2 * 75 = 150 m.
• Therefore, the correct option is (d).
Why the other options are wrong
- (a) 40 m
- 40 m is incorrect because it does not account for the cumulative distance of multiple round trips to increasingly distant apples.
- (b) 50 m
- 50 m is incorrect because it likely represents only the one-way distance to the last apple plus some partial return, ignoring the full round trips for all six apples.
- (c) 75 m
- 75 m is incorrect because it represents only the one-way sum of distances to all apples, failing to double the value for the return trips to the bucket.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.