A man covered a certain distance at some speed. Had he moved 3 kmph faster, he…

2023

A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

  1. A.

    56

  2. B.

    35

  3. C.

    34

  4. D.

    40

Attempted by 2 students.

Show answer & explanation

Correct answer: D

Step-by-Step Solution

  1. Define Variables: Let the original speed be S (kmph) and the original time be T (hours). The distance D is given by D = S × T.

  2. Set up the equations based on the conditions:

    • Condition 1: If speed increases by 3 kmph, time decreases by 40 minutes (40/60 = 2/3 hours). D = (S + 3)(T - 2/3) Since D = ST, we have: ST = (S + 3)(T - 2/3) ST = ST - (2/3)S + 3T - 2 3T - (2/3)S = 2 => 9T - 2S = 6 (Equation 1)

    • Condition 2: If speed decreases by 2 kmph, time increases by 40 minutes (2/3 hours). D = (S - 2)(T + 2/3) ST = ST + (2/3)S - 2T - 4/3 (2/3)S - 2T = 4/3 => 2S - 6T = 4 (Equation 2)

  3. Solve the system of equations:

    • Add (Equation 1) and (Equation 2): (9T - 2S) + (2S - 6T) = 6 + 4 3T = 10 T = 10/3 hours.

    • Substitute T = 10/3 into (Equation 2): 2S - 6(10/3) = 4 2S - 20 = 4 2S = 24 S = 12 kmph.

  4. Calculate Distance: D = S × T = 12 × (10/3) = 40 km.

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