Time and Distance | Arithmetic aptitude | Discussion Page

What is the usual speed of the train ?

I. The speed of the train is increased by 35 km/hr to reach the destination 150 km away in time.

II. The train is late by 30 minutes.

A) I alone sufficient while II alone not sufficient to answer

B) II alone sufficient while I alone not sufficient to answer

C) Either I or II alone sufficient to answer

D) Both I and II are not sufficient to answer

E) Both I and II are necessary to answer

Option E

Let the usual speed of the train be $x$ kmph.

Time taken to cover 150 km at usual speed $=\frac{150}{x}$ hrs.

I. Time taken at increased speed $=\frac{150}{x+25}$ hrs.

II. $\frac{150}{x}-\frac{150}{(x+25)}$ $=\frac{30}{60}$ .

$\Leftrightarrow$ $\frac{1}{x}-\frac{1}{(x+25)}$ $=\frac{1}{300}$

$\Leftrightarrow$ $\left[(x+25)-x\right]\times 3000$ $=x(x+25)$

$\Leftrightarrow$ $x^{2}+25x-7500=0$

$\Leftrightarrow$ $(x+100)(x-75)=0$

$\Leftrightarrow x=75$ .

Thus, I and II together give the answer.

$\therefore$ Correct answer is (E).

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