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Home Aptitude Time and Distance See What Others Are Saying!
  • Question
  • Two ladies simultaneousely leave cities A and B connected by a strainght road and travel towards each other. The first lady travels 2km/h faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?


  • Options
  • A. 5 km,3 km
  • B. 7 km, 5 km
  • C. 8 km, 6 km
  • D. 16 km, 14 km

  • Correct Answer
  • 8 km, 6 km 

    Explanation

    Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
    Total distance = 24 km

    For first lady, Speed = Distance/Time
    v + 2 = 24/t ...(i)

    Let time taken by first lady to cover distance of 24 km be t h.
    Then, time taken by second lady to cover same distance will be(t + 1)h.
    For second lady, Speed =Distance/time
    v = 24/(t + 1) ...(ii)

    Form Eqs.(i) and (ii), we get
    24/t - 2 = 24/(t + 1)
    ? (24 - 2t)/t = 24/(t + 1)
    ? (24 - 2t)(t + 1) = 24t
    ? 24t - 2t2 + 24 - 2t = 24t
    ? 2t2 + 2t - 24 = 0
    ? t2 + t - 12 = 0
    ? t2 + 4t - 3t - 12 = 0
    ? t(t + 4) -3(t + 4) = 0
    ? (t - 3)(t + 4) = 0
    ? t = 3, -4
    ? t = 3 (t ?- 4)
    ? The distance travelled by the first lady in one hour
    = 24/t = 24/3 = 8 km
    And distance travelled by the second lady in one hour
    = 24/t + 1
    = 24/3 + 1 = 6 km


  • More questions

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      A train 300 meters long passes a standing man is 15 seconds. The speed of the train is?

    • Options
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    • 2. 
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    • 3. 46080, 3840, 384, 48, 24, 2, 1

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    • 4. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

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