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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. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
- 9 km/hour
- 10 km/hour
- 11 km/hour
- 12 km/hour
Answer: Option D
Explanation:
We need to calculate the distance, then we can calculate the time and finally our answer.
Lets solve this,
Let the distance travelled by x km
Time = Distance/Speed
\begin{aligned}
\frac{x}{10} - \frac{x}{15} = 2 \\
\text{[because, 2 pm - 12 noon = 2 hours]} \\
3x - 2x = 60 \\
x = 60.
Time = \frac{Distance}{Speed} \\
Time @ 10km/hr = \frac{60}{10} = 6 hours
\end{aligned}
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.
He have to reach at 1 P.M. i.e, in 5 hours
So, Speed = 60/5 = 12 km/hr
2. A car moves at 80 km/hr. What is the speed of the car in meters per second ?
- \begin{aligned} 20\frac{2}{9} m\sec \end{aligned}
- \begin{aligned} 22\frac{2}{9} m\sec \end{aligned}
- \begin{aligned} 24\frac{2}{9} m\sec \end{aligned}
- \begin{aligned} 26\frac{2}{9} m\sec \end{aligned}
Answer: Option B
Explanation:
\begin{aligned}
Speed = \left(80*\frac{5}{18}\right) m/sec \\
= \frac{200}{9} m/sec \\
= 22\frac{2}{9} m\sec
\end{aligned}
3. Ram and Sham are running a race, Ram runs 25% faster than Sham and is able to allow Sham a lead of 7 meters to end a race in dead heat. Find the distance of the race.
- 32 meters
- 35 meters
- 39 meters
- 40.5 meters
Answer: Option B
Explanation:
Important to Note first - Dead Head means - run or finish a race at exactly level or at same time.
From question it is clear that Ram runs faster than Sham by 25%,
So if Sham runs 100 meter in a given time then Ram will run 125 meter in that time.
So if Sham runs 4 meter then Ram will run 5 meter in given time (divide both by 25)
=> Ram can give Sham a lead of 1 meter in 5 meter race to finish race in dead heat.
Ratio of length of start given : length of race :: 1 : 5
As per question, start was given of 7 meter, So,
Length of race was 7 * 5 = 35.
4. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
- 15 hours
- 16 hours
- 17 hours
- 18 hours
Answer: Option C
Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
5. 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}
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