Question : A person travels a distance of 240 km, partly by train and the rest by bus. He takes $3 \frac{1}{2}$ hours if he travels 150 km by train and the rest by bus. If he travels 140 km by bus and the rest by train, he takes $3 \frac{2}{3}$ hours. What is the speed of the train?
Option 1: 80 km/hr
Option 2: 70 km/hr
Option 3: 75 km/hr
Option 4: 72 km/hr
Correct Answer: 75 km/hr
Solution :
Let the speed of the train be $x$ and the speed of the bus be $y$.
According to the question,
$\frac{150}{x} + \frac{90}{y} = \frac{7}{2}$
⇒ $300y +180x = 7xy$......................................(1)
Now,
$\frac{140}{y} + \frac{100}{x} = \frac{11}{3}$
⇒ $420x + 300y = 11xy$.....................................(2)
Subtracting equation (1) from equation (2), we get
⇒ $240x = 4xy$
⇒ $60 = y$
Speed of the bus = 60 km/hr
From equation (1),
$\frac{150}{x} + \frac{90}{60} = \frac{7}{2}$
⇒ $\frac{150}{x} = \frac{7}{2}- \frac{3}{2}$
⇒ $\frac{150}{x} = \frac{4}{2}$
⇒ $x = 75$
Hence, the correct answer is 75 km/hr.
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