Question : A man travelled a distance of 110 km in 11 hours. He travelled some distance on foot at 6 km/hr and the remaining distance on a bicycle at 14 km/hr. What is the distance travelled on a bicycle?
Option 1: 66 km
Option 2: 99 km
Option 3: 77 km
Option 4: 88 km
Correct Answer: 77 km
Solution :
Let the distance travelled on foot as \(x\) km and the distance travelled on bicycle as \(110 - x\) km.
The time taken to travel on foot is \(\frac{x}{6}\) hours and the time taken to travel on bicycle is \(\frac{110 - x}{14}\) hours.
Given that the total time taken is 11 hours,
$⇒\frac{x}{6} + \frac{110 - x}{14} = 11$
\(⇒7x + 3(110 - x) = 462\)
\(⇒x = 33\)
The distance travelled on foot is 33 km.
Therefore, the distance travelled by bicycle = 110 – 33 = 77 km
Hence, the correct answer is 77 km.
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