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Question Detail
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
1. 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}
2. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
- 50 meter
- 100 meter
- 110 meter
- None of above
Answer: Option B
Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =
\begin{aligned}
\frac{1}{60}*6 = \frac{1}{10} \\
= 100 meters
\end{aligned}
So distance between them after 6 minutes = 200 - 100
= 100 meters
3. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
- 200 Km
- 222 Km
- 224 Km
- 248 Km
Answer: Option C
Explanation:
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
4. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.
- 70.11 km/hr
- 71.11 km/hr
- 72.11 km/hr
- 73.11 km/hr
Answer: Option B
Explanation:
We know Time = Distance/speed
So total time taken =
\begin{aligned}
\left(\frac{160}{64}+\frac{160}{80}\right) \\
= \frac{9}{2} hours \\
\text{ Time taken for 320 Km = } \\
320*\frac{2}{9} = 71.11 km/hr
\end{aligned}
5. A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
- 44 km/hour
- 46 km/hour
- 48 km/hour
- 50 km/hour
Answer: Option C
Explanation:
Speed while going = 40 km/hr
Speed while returning = 150% of 40 = 60 km/hr
Average speed =
\begin{aligned}
\frac{2xy}{x+y} \\
= \frac{2*40*60}{40+60} = \frac{4800}{100} \\
= 48 Km/hr
\end{aligned}
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