On one side of a 1·01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?

(a) 40 m
(b) 40·4 m ✓ UPSC's answer
(c) 50 m
(d) 50·5 m

Why the answer is (b)

• The total length of the road is 1.01 km, which converts to 1010 meters.

• With 101 plants planted at equal distances on one side, there are 100 equal intervals between them (since the number of intervals is always one less than the number of plants).

• The distance between any two consecutive plants is calculated by dividing the total length by the number of intervals: 1010 m / 100 = 10.1 m.

• The question asks for the total distance between 5 consecutive plants, which corresponds to the span covering 4 intervals (from the 1st to the 5th plant).

• Multiplying the interval distance by 4 gives 10.1 m × 4 = 40.4 m.

• Therefore, the correct total distance is 40.4 m, matching option (b).

Why the other options are wrong

(a) 40 m: Option (a) is incorrect because it assumes the distance between 5 plants is 40 m, which would require an interval of 10 m, but the actual interval is 10.1 m.
(c) 50 m: Option (c) is incorrect because it calculates the distance for 5 intervals (50 m) instead of the 4 intervals spanned by 5 consecutive plants.
(d) 50·5 m: Option (d) is incorrect because it calculates the distance for 5 intervals using the 10.1 m interval length (50.5 m), rather than the 4 intervals between 5 plants.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.