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Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60km by train and the remaining by bus. If she travels 100km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

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Speed of the train is:

40 km / hr

and speed of bus:

90 km / hr

Speed of the train is:

50 km / hr

and speed of bus:

60 km / hr

Speed of the train is:

70 km / hr

and speed of bus:

1120 km / hr

Speed of the train is:

60 km / hr

and speed of bus:

80 km / hr

answer is D.

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Detailed Solution

Suppose the speed of the train = x km/hr
Speed of the bus = y km/hr.
As we know the formula for time.

Time = \frac{Distance}{Speed}

Total distance = 300 km
Roohi covers 60 km by train Here,
The distance she travel by bus=300 − 60 = 240.
As, it take 4 hours for total journey, so

\frac{60}{x} + \frac{240}{y} = 4

Now, if Roohi travel 100 km by train, and (300 − 100 = 200) by bus, then it takes 10 minutes more. Thus,

\frac{100}{x} + \frac{200}{y} = 4 + \frac{10}{60}

\Rightarrow \frac{100}{x} + \frac{200}{y} = \frac{25}{6}

Suppose,

\frac{1}{x} = u

and

\frac{1}{y} = v

So, the equations become,

60 u + 240 v = 4 \dots \dots \dots \dots \dots \dots \dots . . (1)

100 u + 200 v = \frac{25}{6} \dots \dots \dots \dots \dots \dots \dots \dots . . (2)

Multiply (1) by 5 and (2) by 6 we get

\begin{matrix} 300 u + 1200 v = 20 \dots \dots \dots \dots \dots \dots \dots \dots (3) \\ 600 u + 1200 v = 25 \dots \dots \dots \dots \dots \dots \dots \dots (4) \end{matrix}

Eliminate equation (3) from (4), we get,

\begin{matrix} 300 u = 5 \\ \Rightarrow u = \frac{5}{300} = \frac{1}{60} \end{matrix}

Put the value of u in eq. (1) We get,

\Rightarrow 60 \times \frac{1}{60} + 240 v = 4

\Rightarrow 1 + 240 v = 4

\Rightarrow 240 v = 4 - 1 = 3

\Rightarrow 240 v = 3

\Rightarrow v = \frac{3}{240} = \frac{1}{80}

Now, we find the value of u and v

\frac{1}{x} = u = \frac{1}{60}

∴ x = 60

And

\frac{1}{y} = v = \frac{1}{80}

∴ y = 80

Hence, the speed of the bus = 80 km/h
Speed of train = 60 km/h.
Correct option is 4.

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