A passenger train takes 3(1/2) hours less for a journey of 360 km , if it's…
2024
A passenger train takes 3(1/2) hours less for a journey of 360 km , if it's speed is increased by 35 kmph from its normal speed . The normal speed ( in kmph ) is
- A.
45
- B.
55
- C.
67
- D.
39
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Correct answer: A
Answer: 45
Let the normal speed be x kmph. Time for 360 km at speed x = 360/x hours; at speed x+35 = 360/(x+35) hours.
Given the faster train takes 3.5 hours less: 360/x - 360/(x+35) = 7/2.
Multiply both sides by 2x(x+35): 720(x+35) - 720x = 7x(x+35). The left simplifies to 25200, so 25200 = 7x(x+35).
Divide by 7 and rearrange: x^2 + 35x - 3600 = 0. Factor: (x - 45)(x + 80) = 0, so x = 45 or x = -80. Discard the negative root; x = 45 kmph.
Check: time at 45 kmph = 360/45 = 8 hours; time at 80 kmph = 360/80 = 4.5 hours; difference = 3.5 hours, which matches the given.