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Question Detail
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.
1. A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
- 60 km/hr
- 100 km/hr
- 110 km/hr
- 120 km/hr
Answer: Option D
Explanation:
Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour
2. 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
3. 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}
4. 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
5. A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?
- 7:15 am
- 7:30 am
- 7: 42 am
- 7:50 am
Answer: Option C
Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 7:30 + 12 mins = 7:42
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