Question : Train A takes 45 minutes longer than Train B to travel a distance of 450 km. Due to engine trouble, the speed of train B falls by a quarter, so it takes 30 minutes more than train A to complete the same journey. What is the speed of train A (in km/h)?
Option 1: 90
Option 2: 120
Option 3: 100
Option 4: 110
Correct Answer: 100
Solution :
Let train B take $t$ min, and train A take $(t + 45)$ min.
Due to engine failure, train B takes 30 min more than train A.
So train B takes $(t + 75)$ minutes to complete the journey.
Let the original speed of train B be $v$
.
After the reduction in the speed =$v-\frac{v}{4}=\frac{3}{4}v$
So, $\frac{450}{\frac{3}{4}v}=t+75$ ----(1)
And $\frac{450}{v}=t$ ----(2)
From equation 1 and 2, we get,
$\frac{4t}{3}=t+75$
⇒ $t=225$ min
So, train A taken $(t + 45) = 225 + 45 = 270$ min
Hence, speed of train A = $450×\frac{60}{270}=100$ km/h.
Hence, the correct answer is 100.
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