Multiple choice

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes 4 hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B 2 hours before Narayan reaches B. The speed of Partha (in km per hour) is

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Vp and Vn be speeds. 60/Vp = 60/Vn + 4. Also, 30/Vp = 60/Vn - 2. From the second, 60/Vp = 120/Vn - 4. Equating the two expressions for 60/Vp: 60/Vn + 4 = 120/Vn - 4, so 8 = 60/Vn, Vn = 7.5. Then 60/Vp = 60/7.5 + 4 = 8 + 4 = 12, so Vp = 5.

AI explanation

Let Narayan take T hours to travel the 60 km distance, meaning Partha takes T + 4 hours. Partha reaches the 30 km midpoint in (T + 4) divided by 2 hours, which equals T minus 2 based on the given condition. Solving the equation (T + 4) divided by 2 equals T minus 2 yields T equals 8. Partha's total time is 12 hours, so her speed is 60 divided by 12, which is 5 km per hour.

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