711. Walking at 80% of his usual speed, a man is 10 mins late to his office. Find the usual time taken by hime to reach his office.
A. 20 minutes
B. 30 minutes
C. 40 minutes
D. 50 minutes
usual speed be x kmph
usual travel time be t hours
distance to office be d km d=xt d=(0.8x)*[t+(10/60)] xt=0.8xt+(2x/15) Solving,
712. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?
Let the speed of the faster train be x miles per hour and
the distance travelled by it when it meets the slower train be y miles. Time taken by the faster train to cover y miles
= Time taken by the slower train to cover (287-y) miles
= 3.5 hours (y/x) = (287-y)/(x-6) = 3.5 Solving, x = 44 miles/hr
713. Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.
X ———— Y ———— Z
If ‘d’ is the distance between X and Y, then ‘d’ is the distance between Y and Z.
Now the total time for the batsman to row from X to Z is 4 hours. Therefore, time to row from X to Y is 2 hours.
Also the time for the boats man to row from X to Y and back is 10 hours. Hence, time required to row from Y to X is 8 hours.
If, a: speed of boats man in still water
b: speed of the river
d/(a + b) = 2; d/(a – b) = 8
2*(a + b) = 8*(a – b)
a + b = 4a – 4b
3a = 5b
a:b = 5:3
714. A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?
A. 22 km/hr
B. 33 km/hr
C. 66 km/hr
D. 44 km/hr
The relative speed of A and B is 6 km/hr = 1.67 m/s
As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.
Therefore, at t = 11, d = 1.67 * 11
d = 18.33 m
v = d/t = 18.33/1 = 18.33m/s
v = 66 km/hr
715. A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
A. 70.24 km/hr
B. 74. 24 km/hr
C. 71.11 km/hr
D. 72.21 km/hr
716. A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is_________?
A. 11 hrs
B. 8 hrs 45 min
C. 7 hrs 45 min
D. 9 hts 20 min
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way – 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
717. In a journey of 24 miles, two thirds of the distance was travelled with a speed of 40 mph and the remaining with 60 mph. How much time did the journey take?
A. 14.4 minutes
B. 20 minutes
C. 28.8 minutes
D. 32 minutes
(2/3)*24=16 miles Time taken to cover the first 16 miles
= (16/40) hours
= 24 minutes Time taken to cover the next 8 miles
= (8/60) hours
= 8 minutes Time taken for the entire journey
= 32 minutes
718. A man travels a distance of 2 km by walking at a speed of 6 km/hr. He returns back at a speed of 4 km/hr. What is his average speed?
A. 4.5 kmph
B. 4.8 kmph
C. 5 kmph
D. 5.1 kmph
Time taken for the forward journey
= 2/6 = (1/3) hrs Time taken for the return journey
= 2/4 = (1/2) hrs Total time = 5/6 hrs Average speed = 4/(5/6) = 24/5 = 4.8kmph
719. A man rows at a speed of 6 km/hr in still water. If the time taken to row a certain distance upstream is 4 times the time taken to row the same distance downstream, what is the speed of the river?
A. 1.8 km/hr
B. 3 km/hr
C. 3.6 km/hr
D. 4 km/hr
Let x be the speed of the river.
Ds = (6 + x) km/hr; Us = (6 – x) km/hr
If t hours is the time to row downstream then 4t hours is the time to row upstream.
(6 + x)*t = (6 – x)*4t
6 + x = 24 – 4x
x = 3.6 km/hr
720. Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?
A. 0.60 minutes
B. 0.36 minutes
C. 0.78 minutes
D. 0.42 minutes
Total distance = addition of length of the two trains = 140 + 120 = 260 metres
As the two trains are travelling in the same direction, their relative speed is:
v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min
t = 260/ 1000*3
t = 0.78 minutes