Question : A man covers half part of a certain distance at 60 km/hr. He covers 40% of the remaining distance at the speed of 12 km/hr and covers the rest of the distance at the speed of 18 km/hr. What is his average speed for the entire journey?
Option 1: 24 km/hr
Option 2: $\frac{58}{3}$ km/hr
Option 3: 36 km/hr
Option 4: 40 km/hr
Correct Answer: 24 km/hr
Solution :
Let the total distance be 100 km.
Half distance = $\frac{100}{2}$ = 50 km
Speed = 60 km/hr
Time taken to cover half the distance = $\frac{50}{60}$ = $\frac{5}{6}$
Remaining distance = 50 km
Distance = 40% of the remaining distance = $\frac{40}{100}×50$ = 20 km
Speed = 12 km/hr
Time taken to cover 40% of the remaining distance = $\frac{20}{12}$ = $\frac{5}{3}$
Distance = 60% of the remaining distance = $\frac{60}{100}×50$ = 30 km
Speed = 18 km/hr
Time taken to cover 60% of the remaining distance = $\frac{30}{18}$ = $\frac{5}{3}$
Average speed = $\frac{\text{total distance}}{\text{total time}}$
= $\frac{100}{\frac{5}{6}+\frac{5}{3}+\frac{5}{3}}$
= $\frac{100}{\frac{25}{6}}$
= 24 km/hr
Hence, the correct answer is 24 km/hr.
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