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IPMAT Rohtak 2019 PYQsQuantitative Ability. Free, no login required.

Arithmetic

past year questions, IPMAT Rohtak 2019

Time, Speed & Distance

past year questions, Arithmetic, IPMAT Rohtak 2019

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.

Solution

✅ 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,

450A−450B=4560\frac{450}{A} - \frac{450}{B} = \frac{45}{60}

⇒450(1A−1B)=4560\Rightarrow 450(\frac{1}{A} - \frac{1}{B}) = \frac{45}{60}

⇒10(1A−1B)=160\Rightarrow 10(\frac{1}{A} - \frac{1}{B}) = \frac{1}{60}

⇒1A−1B=1600\Rightarrow \frac{1}{A} - \frac{1}{B} = \frac{1}{600} ---- (1)(1)

And

4503B/4−450A=3060\frac{450}{3B/4} - \frac{450}{A} = \frac{30}{60}

⇒43B−1A=1900\Rightarrow \frac{4}{3B} - \frac{1}{A} = \frac{1}{900} ---- (2)(2)

Adding both the equations we get

43B−1B=1600+1900\frac{4}{3B} - \frac{1}{B} = \frac{1}{600} + \frac{1}{900}

⇒13B=51800\Rightarrow \frac{1}{3B} = \frac{5}{1800}

⇒1B=5600\Rightarrow \frac{1}{B} = \frac{5}{600}

⇒1B=1120\Rightarrow \frac{1}{B} = \frac{1}{120}

Putting this value in equation 1 we get

1A=1600+1120\frac{1}{A} = \frac{1}{600} + \frac{1}{120}

⇒1A=6600\Rightarrow \frac{1}{A} = \frac{6}{600}

⇒1A=1100\Rightarrow \frac{1}{A} = \frac{1}{100}

⇒A=100\Rightarrow A = 100 km/hr

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

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