Question : With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is 15 minutes late. The total journey is:
Option 1: 30 km
Option 2: 40 km
Option 3: 70 km
Option 4: 80 km
Correct Answer: 70 km
Solution :
The average speed of a train 40 km/hr, reaches its destination in time.
The new average speed is 35 km/hr.
Time = 15 minutes = $\frac{15}{60} = \frac{1}{4}$ hours
Let the distance travelled by the train be $d$ km.
According to the question,
$\frac{d}{35}-\frac{d}{40}=\frac{1}{4}$
⇒ $\frac{8d-7d}{280}=\frac{1}{4}$
⇒ $d=\frac{280}{4}$
$\therefore d= 70$ km
Hence, the correct answer is 70 km.
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