Question : A bus starts from a bus stand after every 50 minutes in the same direction. Mohit is walking in the opposite direction at 50 km/hr. If Mohit meets each bus in 10 minutes, then what is the speed of the bus?
Option 1: 14.5 km/hr
Option 2: 15 km/hr
Option 3: 12.5 km/hr
Option 4: 10.5 km/hr
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Correct Answer: 12.5 km/hr
Solution :
Let the speed of the bus be $x$ km/hr
According to the question,
Mohit meets each bus in 10 minutes
⇒ Distance covered by bus in (50 - 10) = 40 minutes $=$ The distance travelled by Mohit in 10 minutes
⇒ Distance covered by the bus in $\frac{40}{60}\ \mathrm{hr}$ = The distance traveled by Mohit in $\frac{10}{60}\ \mathrm{hr}$
⇒ $\frac{40x}{60} = 50 \times \frac{10}{60}$
⇒ $x = 12.5\ \mathrm{km/hr}$
Hence, the correct answer is 12.5 km/hr.
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