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
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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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