- Tue Sep 18, 2018 8:57 pm#755
সম্বলিত সিনিয়র অফিসার লিখিত পরীক্ষার জন্য অনুশীলন ম্যাথ। সমাধান সহ দেওয়া হল।
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১) Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B
solution:
1.x/100-(x/120+10/60)=5/60
=>x=150 km.
২) M. Poirot and Miss Marple walk into a turned-off escalator to realize that he is able to walk 3 steps during the time she needs to walk only 2. When the escalator is turned-on and it is already working at constant speed, M. Poirot enters again the escalator to realize he needs to take 25 steps to go through it, while Miss Marple realizes she needs only 20 steps to reach its end (at the very same conditions). How many steps are there on the escalator?
Solution:
২).Let speed of M.Poirot be p and that of Miss Marple be m
we are given p=3 and m=2
let speed of escalator be e
when p and m are on escalator their respective speeds are 3+e and 2+e
we are also given that time taken by p (tp) = 25/3
and time taken by m (tm) = 20/2 = 10
distance = number of steps = speed * time
AtQ, (e+3)*25/3 = (e+2)*10
=> e= 3 Replacing e = 3 in (e+3)*25/3 distance =50
৩) Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system
Solution:
3.20x+40(x-3)= 240
solving equation
x= 6
so, 8+6= 14 which is 2 pm
৪) Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking
Solution:
(4)Let t be the time that the man spends walking. Let w be the man's speed of walking. Let v be the car's speed. Let d be the distance from the train station to the couple's home.
Then t + (d-wt)/v = d/v + 1 - (20/60)
[Time taken by man to walk + time taken by the couple to cover the rest of the distance in the car = Time taken by the couple to cover the entire distance from the station to their home in the car + one extra hour as the man had arrived an hour early - 20 minutes earlier that they reach]
Also wt/v + t = 1
[Time taken by man to walk from the station to where his wife picks him up + Time that the wife would have taken to go to the station had the man not walked = 1 hour]
Solving these two equations for t (note that d/v gets eliminated and wt/v gets substituted),
we get 2t = 5/3
=> t = 5/6 hours or (5/6)*60 = 50 minutes
৫) Two heavily loaded sixteen-wheeler transport trucks are 770 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
Solution:
5)rest 770-90=680
let time t atq,90t+80t=680
t=4
90+90*4-320=130 km
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১) Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B
solution:
1.x/100-(x/120+10/60)=5/60
=>x=150 km.
২) M. Poirot and Miss Marple walk into a turned-off escalator to realize that he is able to walk 3 steps during the time she needs to walk only 2. When the escalator is turned-on and it is already working at constant speed, M. Poirot enters again the escalator to realize he needs to take 25 steps to go through it, while Miss Marple realizes she needs only 20 steps to reach its end (at the very same conditions). How many steps are there on the escalator?
Solution:
২).Let speed of M.Poirot be p and that of Miss Marple be m
we are given p=3 and m=2
let speed of escalator be e
when p and m are on escalator their respective speeds are 3+e and 2+e
we are also given that time taken by p (tp) = 25/3
and time taken by m (tm) = 20/2 = 10
distance = number of steps = speed * time
AtQ, (e+3)*25/3 = (e+2)*10
=> e= 3 Replacing e = 3 in (e+3)*25/3 distance =50
৩) Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system
Solution:
3.20x+40(x-3)= 240
solving equation
x= 6
so, 8+6= 14 which is 2 pm
৪) Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking
Solution:
(4)Let t be the time that the man spends walking. Let w be the man's speed of walking. Let v be the car's speed. Let d be the distance from the train station to the couple's home.
Then t + (d-wt)/v = d/v + 1 - (20/60)
[Time taken by man to walk + time taken by the couple to cover the rest of the distance in the car = Time taken by the couple to cover the entire distance from the station to their home in the car + one extra hour as the man had arrived an hour early - 20 minutes earlier that they reach]
Also wt/v + t = 1
[Time taken by man to walk from the station to where his wife picks him up + Time that the wife would have taken to go to the station had the man not walked = 1 hour]
Solving these two equations for t (note that d/v gets eliminated and wt/v gets substituted),
we get 2t = 5/3
=> t = 5/6 hours or (5/6)*60 = 50 minutes
৫) Two heavily loaded sixteen-wheeler transport trucks are 770 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
Solution:
5)rest 770-90=680
let time t atq,90t+80t=680
t=4
90+90*4-320=130 km
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