UPSC Prelims 2014 CSAT Paper II · Q50 of 65 Basic Numeracy medium

A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is

  1. (a) 3 km
  2. (b) 4 km
  3. (c) 5 km ✓ UPSC's answer
  4. (d) 6 km

Why the answer is (c)

• Let the distance be d km and the scheduled travel time be T hours.

• At 5 km/hr, time taken is d/5, which is 3 minutes late, so d/5 = T + 3/60.

• At 6 km/hr, time taken is d/6, which is 7 minutes early, so d/6 = T - 7/60.

• Subtracting gives d/5 - d/6 = 3/60 + 7/60 = 10/60 = 1/6 hour.

• Thus d/30 = 1/6, so d = 5 km, which is option (c).

Why the other options are wrong

(a) 3 km
For 3 km, the time difference between 5 km/hr and 6 km/hr is 6 minutes, not the required 10 minutes.
(b) 4 km
For 4 km, the time difference between 5 km/hr and 6 km/hr is 8 minutes, not the required 10 minutes.
(d) 6 km
For 6 km, the time difference between 5 km/hr and 6 km/hr is 12 minutes, not the required 10 minutes.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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