IPMAT Rohtak 2019 (QA) - Train A takes 45 minutes more than train B to travel 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. Find the speed of Train A. | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time, Speed & Distance

Medium

Train A takes 45 minutes more than train B to travel 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. Find the speed of Train A.

120 km/hr

110 km/hr

100 km/hr

90 km/hr

Correct Option: 3

Let the speed of A be A km/hr and the speed of B be B km/hr

According to the question,

\frac{450}{A} - \frac{450}{B} = \frac{45}{60}

\Rightarrow 450(\frac{1}{A} - \frac{1}{B}) = \frac{45}{60}

\Rightarrow 10(\frac{1}{A} - \frac{1}{B}) = \frac{1}{60}

\Rightarrow \frac{1}{A} - \frac{1}{B} = \frac{1}{600}

----

(1)

And

\frac{450}{3B/4} - \frac{450}{A} = \frac{30}{60}

\Rightarrow \frac{4}{3B} - \frac{1}{A} = \frac{1}{900}

----

(2)

Adding both the equations we get

\frac{4}{3B} - \frac{1}{B} = \frac{1}{600} + \frac{1}{900}

\Rightarrow \frac{1}{3B} = \frac{5}{1800}

\Rightarrow \frac{1}{B} = \frac{5}{600}

\Rightarrow \frac{1}{B} = \frac{1}{120}

Putting this value in equation 1 we get

\frac{1}{A} = \frac{1}{600} + \frac{1}{120}

\Rightarrow \frac{1}{A} = \frac{6}{600}

\Rightarrow \frac{1}{A} = \frac{1}{100}

\Rightarrow A = 100

km/hr

\therefore

The speed of Train A (in km/hr) is 100.