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Question Detail
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ?
- 3 hours
- 2.4 hours
- 1.4 hours
- 1 hour
Answer: Option D
Explanation:
Let the duration of the flight be x hours.
Then
\begin{aligned}
\frac{600}{x}-\frac{600}{x + \frac{1}{2}} = 200 \\
\frac{600}{x}-\frac{1200}{2x+1} = 200 \\
x(2x+1) = 3 \\
2x^2 + x - 3 = 0 \\
=> (2x+3)(x-1)=0
\end{aligned}
Neglecting the negative value for x we get x = 1
1. A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
- 16 km/hr
- 17 km/hr
- 18 km/hr
- 19 km/hr
Answer: Option C
Explanation:
\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 750 meter \\
Time = \text{2 min 30 sec} = 150 sec \\
Speed = \frac{750}{150} = 5 m/sec \\
=> 5*\frac{18}{5} km/hr = 18 km/hr
\end{aligned}
2. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
- 50 km/hr
- 60 km/hr
- 65 km/hr
- 70 km/hr
Answer: Option B
Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km
New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph
3. 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
- 11:9
- 13:9
- 17:9
- 21:9
Answer: Option A
Explanation:
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9
4. The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?
- 83.5 km/hr
- 84.5 km/hr
- 86.5 km/hr
- 87.5 km/hr
Answer: Option D
Explanation:
Let the speeds of two trains be 7X and 8X km/hr.
\begin{aligned}
8X = \frac{400}{4} \\
=> X = 12.5 Km/hr
\end{aligned}
So speed of first train is 12.5*7 = 87.5 km/hr
5. An athlete runs 200 meters in 24 seconds. His speed is ?
- 10 km/hr
- 17 k/hr
- 27 km/hr
- 30 km/hr
Answer: Option D
Explanation:
\begin{aligned}
Speed = \frac{Distance}{Time} \\
= \frac{200}{24}m/sec = \frac{25}{3} m/sec \\
\frac{25}{3}*\frac{18}{5} km/hr = 30 km/hr
\end{aligned}
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