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Question Detail
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
1. 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
2. A man is walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge is
- 1000 meters
- 1050 meters
- 1200 meters
- 1250 meters
Answer: Option D
Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
\begin{aligned}
Speed = 5* \frac{5}{18} = \frac{25}{18}m/sec \\
Time = 15*60 seconds = 900 seconds \\
Distance = Time * Speed \\
Distance = \frac{25}{18}*900 = 1250 meter
\end{aligned}
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. 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.
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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