CDS 2026 (I) Elementary Mathematics, question 26

Topic: HCF and LCM

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Q26

What is the greatest possible speed at which a person can walk 13.313.3 km and 20.920.9 km so that the time (in hours) required in each case is a whole number ?

  1. (a) 1.71.7 km/h
  2. (b) 1.91.9 km/hCorrect answer
  3. (c) 2.12.1 km/h
  4. (d) 2.32.3 km/h

Solution.

Answer: (b) 1.91.9 km/h

  1. For both travel times to be integers, the speed must be a common divisor of 13.3 and 20.9.
  2. After multiplying by 10,gcd⁡(133,209)=1910,\gcd(133,209) = 19, so the greatest speed is 19/10=1.9km/h19/10 = 1.9km/h.
  3. The travel times are 7 hours and 11 hours, confirming the result.