A car travels 50% faster than a bike. Both start at the same time from A to B. The car reaches 25 minutes earlier than the bike. If the distance from A to B is 100 km, find the speed of the bike.
A. 120 kmph
B. 100 kmph
C. 80 kmph
D. 75 kmph
Answer: Option C
Solution(By Examveda Team)
P __________100km__________Q Let car takes time T hours to reach destination.So, Bike will take $$\left( {{\text{T}} + \frac{{25}}{{60}}} \right)$$ Let speed of the bike = S kmph Speed of Car = S + 50% of S = $$\frac{{3{\text{S}}}}{2}$$ kmph For the both the case distance is constant. And when distance remain constant then time is inversely proportional to speed (As ST + D) So,
$$\eqalign{ & \frac{{ {\frac{{3S}}{2}} }}{{\left( S \right)}} = \frac{{ {T + {\frac{5}{{12}}} } }}{T} \cr & 3T = 2T + \frac{{10}}{{12}} \cr & T = \frac{{10}}{{12}}{\text{hours}} \cr & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{car}} \cr & \frac{{3S}}{2} = \frac{{100}}{{ {\frac{{10}}{{12}}} }} \cr & \frac{{3S}}{2} = 120 \cr & S = 80\,kmph \cr & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{bike}} = 80\,kmph \cr} $$
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Comments ( 2 )
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
Bike speed x and car speed 3x/2
According to the question
100/x = 100/3x/2 +25/60
100/x =200/3x +5/12
100/x - 200/3x = 5/12
100/3x = 5/12
x= 80 km
Sc:sb=150:100
T=100:150=10:15=2:3=50:75
so speed of bike=100/75/60=80 km/hr...(ans)