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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৩ প্রশ্ন

১.
A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 10 km/hr, he covers the same distance in-
  1. ক
    ক) 10 min
  2. খ
    খ) 20 min
  3. গ
    গ) 30 min
  4. ঘ
    ঘ) 40 min
ব্যাখ্যা

Distance = Speed×Time
Distance = (6× 50)/60)km
Distance = 5 km
∴ Required time
= Distance/ Speed
= 5/10 hrs
= 1/2 hrs
= 30 min

২.
With a uniform speed, a car covers a distance in 8 hours. had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?
  1. ক
    ক) 420 km
  2. খ
    খ) 480 km
  3. গ
    গ) 520 km
  4. ঘ
    ঘ) 640 km
ব্যাখ্যা

Let the speed of car be x km/hr
Distance= Speed × Time
Distance = 8x km
According to the question,
⇒ (x+4)×7.5= 8x
⇒ 7.5x+30= 8x
⇒ 8x−7.5x= 30
⇒ 0.5x= 30
⇒x= (30/0.5)= 60 km/hr
Required distance:
= 8 × 60
= 480 km

৩.
Car A travels at the speed of 65 km/hr and reaches its destination in 8 hours. Car B travels at a speed of 70 km/hr and reaches its destination in 4 hours. What is the ratio of the distance covered by car A and car B respectively?
  1. ক
    ক) 7:11
  2. খ
    খ) 13:7
  3. গ
    গ) 7:13
  4. ঘ
    ঘ) 11:7
ব্যাখ্যা

Required ratio:
= (65×8):(70×4)
= 520:280
= 13:7

৪.
If a runner takes as much time in running 20 metres as the car takes in covering 50 metres. The distance covered by the runner during the time the car covers 1 km is -
  1. ক
    ক) 400 metres
  2. খ
    খ) 40 metres
  3. গ
    গ) 440 metres
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

According to the question,
∴ 50 m = 20 m
∴ 1m = 20/50 m
∴ 1000 m = (20/50)×1000 m
= 400 metres

৫.
A boy rides his bicycle 10 km at an average speed of 12 km/hr and travel 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
  1. ক
    ক) 10.4 km/hr
  2. খ
    খ) 10.8 km/hr
  3. গ
    গ) 11.0 km/hr
  4. ঘ
    ঘ) 12.2 km/hr
ব্যাখ্যা

Average speed= Total distance/Total time
Average speed= (10+12)/(10/12)+(12/10)
Average speed= 10.8 km/hr

৬.
A man is walking at a speed of 10 kmph. After every km, he takes rest for 5 minutes. How much time will he take to cover a distance of 5 km?
  1. ক
    ক) 60 min
  2. খ
    খ) 50 min
  3. গ
    গ) 55 min
  4. ঘ
    ঘ) 70 min
ব্যাখ্যা

Time taken by man if he did not stop
= 5 km/10 kmph
= 1/2 hr
= 30 min 
∵Man takes rest for 5 minutes on each km
Total rest time= 5×4= 20 min
Total travelling time:
= 30 min+20 min
= 50 min

৭.
A distance is covered by a cyclist at a certain speed. If a jogger covers half of the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is -
  1. ক
    ক) 1:4
  2. খ
    খ) 4:1
  3. গ
    গ) 1:2
  4. ঘ
    ঘ) 2:1
ব্যাখ্যা

Cyclist:Jogger
Ratio of distance→ 2:1
Ratio of time→ 1:2
Ratio of their speed (Jogger:Cyclist)
= (1/2):(2/1)
= 1:4

৮.
P and Q are 27 km away. Two trains with speed of 24 km/hr and 18 km/hr respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is -
  1. ক
    ক) 126 km
  2. খ
    খ) 81 km
  3. গ
    গ) 48 km
  4. ঘ
    ঘ) 36 km
ব্যাখ্যা

Relative speed= 24-18= 6 km/hr
Time required by faster train to overtake slower train
= 27/6 hr
= 4(1/2) hr
∴ Distance between Q and R:
= 18×4(1/2)
= 81 km

৯.
Two men start together to walk a certain distance, one at 4 km/hr and another at 3 km/hr. The former arrives half an hour before the latter. Find the distance -
  1. ক
    ক) 8 km
  2. খ
    খ) 7 km
  3. গ
    গ) 6 km
  4. ঘ
    ঘ) 9 km
ব্যাখ্যা

If the required distance be x km, then
(x/3)−(x/4)= 1/2
⇒ (4x−3x)/12= 1/2
⇒ x/12= 1/2
⇒ x= 6 km

১০.
A man walk a certain distance and rides back in 4 hours 30 minutes. He could ride both ways in 3 hours. The time required by the man to walk both ways is :
  1. ক
    ক) 4 hours 30 minutes
  2. খ
    খ) 4 hours 45 minutes
  3. গ
    গ) 5 hours
  4. ঘ
    ঘ) 6 hours
ব্যাখ্যা

Time taken to ride one way = 3/2 = 1.5 hrs
Time taken to walk one way:
= 4.5 - 1.5
= 3 hrs
Time taken to walk both way :
= 3×2
= 6 hours

১১.
A is twice fast as B and B is thrice fast as C is. The journey covered by C in 3/2 hours will be covered by A is-
  1. ক
    ক) 15 minutes
  2. খ
    খ) 20 minutes
  3. গ
    গ) 30 minutes
  4. ঘ
    ঘ) 1 hour
ব্যাখ্যা

Let speed of C = X
Then Speed of B = 3X
Then Speed of A = 6X
Ratio of the speed of A and C = 1:6
So, Greater the speed less time taken in journey.
C’s speed is 6 times less than A So A will take
1/6 of the total time taken C to covered same distance.
So, Time taken by A
= 3/(2×6)
= 1/4 hours
= 15minutes

১২.
A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
  1. ক
    ক) 16 km
  2. খ
    খ) 14 km
  3. গ
    গ) 12 km
  4. ঘ
    ঘ) 10 km
ব্যাখ্যা

Let the time in which he traveled on foot = x hour
Time for travelling on bicycle = (9-x) hr
Distance = Speed×Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4x4 = 16 km

১৩.
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.
  1. ক
    ক) 70.11 km/hr
  2. খ
    খ) 71.11 km/hr
  3. গ
    গ) 72.11 km/hr
  4. ঘ
    ঘ) 73.11 km/hr
ব্যাখ্যা

We know Time = Distance/speed
So total time taken = (160/64) + (160/80)
Time taken for 320 Km = 320× (2/9) = 71.11km/hr

১৪.
A monkey tries to ascend a greased pole which has a height of 14 m. He ascends 2 m in first two minutes and slips 1 m in the very next minute. If he continues to ascend in this fashion, how long does he take to reach the top of the pole?
  1. ক
    ক) 26 min
  2. খ
    খ) 24 min
  3. গ
    গ) 22 min
  4. ঘ
    ঘ) 25 min
ব্যাখ্যা

In every two minutes he is able to ascend 1 m.
In this fashion he ascends up to 12 m because when he reaches at the top he does not slip down.
Thus, up to 12 m he takes 12×2=24 min. and for the last 2 m he takes 1 m.
Therefore, total time taken by him is 24+1 = 25 min to reach the top.

১৫.
X and Y start walking towards each other at 10 am at speeds of 3 km/hr and 4 km/hr respectively. They were initially 17.5 km apart. At what time do they meet?
  1. ক
    ক) 2:30 pm
  2. খ
    খ) 11 :30 pm
  3. গ
    গ) 1:30 pm
  4. ঘ
    ঘ) 12 :30 pm
ব্যাখ্যা

Let after T hours they meet
Then, 3T+4T=17.5
T=2.5
Time = 10:00 am + 2.5 hour = 12:30 pm

১৬.
A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is-
  1. ক
    ক) 48 km/hr
  2. খ
    খ) 37 km/hr
  3. গ
    গ) 44 km/hr
  4. ঘ
    ঘ) 45 km/hr
ব্যাখ্যা

Here, 2xy/(x+y) = (2×40×60)/(40+60) = 48

১৭.
In a 1000 m race, A can beat B by 100 m. In a race of 400 m, B can beat C by 40 m. By how many metres will A beat C in a race of 500 m?
  1. ক
    ক) 85 m
  2. খ
    খ) 95 m
  3. গ
    গ) 105 m
  4. ঘ
    ঘ) 115 m
ব্যাখ্যা

A:B = 1000:900
B:C = 400:360 = 100:90 = 900:810
⇒ A:B:C = 1000:900:810
⇒ A:C = 1000:810
⇒ A:C = 500:405
⇒ In a 500 m race, A beats C by (500-405) m = 95 m

১৮.
A team played 40 games in a season and won in 24 of them. What percent of games played did the team win?
  1. ক
    ক) 70%
  2. খ
    খ) 40%
  3. গ
    গ) 60%
  4. ঘ
    ঘ) 35%
ব্যাখ্যা

Number of games played = 40
Number of won games = 24
Percentage of games played = (24/40)× 100
= 60%

১৯.
If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
  1. ক
    ক) 48
  2. খ
    খ) 60
  3. গ
    গ) 54
  4. ঘ
    ঘ) 90
ব্যাখ্যা

When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60×64×150)/(80×80) = 90
Therefore, in a game of 150, R can give 60 points to Q.

২০.
In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
  1. ক
    ক) 86 sec
  2. খ
    খ) 80 sec
  3. গ
    গ) 76 sec
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

B runs 45/2 m in 6 sec.
B covers 300 m in (6x2)/45 x300 sec
= 80 sec

২১.
Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?
  1. ক
    ক) 6.52
  2. খ
    খ) 8.14
  3. গ
    গ) 4.18
  4. ঘ
    ঘ) 5.02
ব্যাখ্যা

Distance to be covered = πD = 40π km
Relative speed of bikers = 16 + 14 = 30 kmph.
Now, time = distance/speed = 40π/30
= 4.18 hrs.

২২.
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
  1. ক
    ক) 20 m
  2. খ
    খ) 25 m
  3. গ
    গ) 22.5 m
  4. ঘ
    ঘ) 9 m
ব্যাখ্যা

Distance covered by B in 9 sec.
=(100/45)x 9m= 20 m.
A beats B by 20 metres.

২৩.
A is 2(1/3) times as fast as B. If A gives B a start of 80 metres, how long should the race course be so that both of them reach at the same time?
  1. ক
    ক) 170 metres
  2. খ
    খ) 140 metres
  3. গ
    গ) 160 metres
  4. ঘ
    ঘ) 150 metres
ব্যাখ্যা

speed of A : speed of B = 7/3:1 = 7:3
It means, in a race of 7 metres, A gains (7−3 ) = 4 metres.
If A needs to gain 80 metres, race should be of (7/4)×80 = 140 metres.