ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Let,
pipe A alone takes x hours to fill the tank.
Then, pipe B take x/2 hours to fill the tank.
and pipe C will take x/4 hours to fill the tank.

ATQ,
(1/x) + (2/x) + (4/x) = 1/5
⇒ 7/x = 1/5
∴ x = 35 hours.

Question: With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

Solution:
Difference between timings = 24 min = 24/60 hr = 2/5 hr.
Let the length of the journey be x km.

Then,
(x/40) - (x/50) = 2/5
Or, (5x - 4x)/200 = 2/5
Or, x/200 = 2/5
Or, x = (25 × 200)
∴ x = 80 km.

∴ The total journey is 80 km.

Question: Four people are running around a circular ground from a point on the circumference at 9.00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again?

Solution:
L.C.M. of 40, 50, 60 and 30
= 600 minutes
= 10 hours
So, they meet again 10 hours after they start.
They meet together again = 9.00 am + 10 hours
= 7.00 pm

Question: Rina and Trina walk from same point in opposite directions at the rate 3 km/hr and 2 km/hr respectively. How far will they be from each other after 3 hrs?

Solution: 
Since Rina and Trina walk in opposite directions.
Distance covered per hour = Relative speed × Time
= (3 + 2) × 1 = 5 km   [opposite direction]

∴ Distance covered in 3 hours = 5 × 3 = 15 km.

Question: A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both pipes are open, in how many hours will the tank is filled?

Solution:
Net part filled in 1 hour = (1/x - 1/y)
= (y - x)/xy hours.

∴ The tank will be filled in = xy/(y - x) hours.

Question: If a train runs at 40 km/hr, it reaches its destination late by 11 minutes but if it runs at 50 km/hr, it is late by 5 min only. The correct time for the train to complete its journey is:

Solution:
Let the correct time to complete the journey be x min

ATQ,
Distance covered in (x + 11) min at 40 km/hr = Distance covered in (x + 5) min at 50 km/hr
⇒ {(x + 11) × 40}/60 = {(x + 5) × 50}/60
⇒ 2(x + 11)/3 = 5(x + 5)/6
⇒ (2x + 22)/3 = (5x + 25)/6
⇒ 15x + 75 = 12x + 132
⇒ 15x - 12x = 132 - 75
⇒ 3x = 57
⇒ x = 57/3
∴ x = 19

The correct time for the train to complete its journey is 19 min.

Question: A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot 4 km/hr and partly on bicycle at 9 km/hr. The distance travelled on foot is:

Solution:
Let the distance travelled on foot be x km
Then,
distance travelled on bicycle = (61 - x) km

So,
x/4 + (61 - x)/9 = 9
⇒ 9x + 4(61 - x) = 9
⇒ 9x + 244 - 4x = 9 × 36
⇒ 5x = 324 - 244
⇒ 5x = 80
⇒ x = 80/5
∴ x = 16 km.

∴ The distance travelled on foot is 16 km.

Question: A tank is 30% full with water. If 18 liters of water is added the tank becomes 3/4 full. What is the capacity of the tank?

Solution:
Let, Capacity of the tank is x Liters.

ATQ,
30% of x + 18 = (3/4) × x
⇒ (30x/100) + 18 = 3x/4
⇒ (3x/10) + 18 = 3x/4
⇒ (3x/4) - (3x/10) = 18
⇒ (15x - 6x)/20 = 18
⇒ 9x = 18 × 20
⇒ 9x = 360
∴ x = 40

∴ The capacity of tank is 40 Liters.

Question: How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction?

Solution:
Total distance covered by the length of both trains = (50 + 75) m = 125 m
And, their relative speed in same direction = (68 - 50) = 18 km/hr

Then, the time to cross each other will be = 125 m/18 km/hr.
= (125 × 3600)/(18 × 1000) s
= 25 sec

Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

Solution:
Distance = (240 x 5) = 1200 km.

Speed = Distance/Time
Or, Speed = 1200/(5/3) km/hr. 

 ∴ Required speed = 1200/(5/3) km/hr
= 720 km/hr.

Question: A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken;
= 1/6 : 1/3 : 1 = 1 : 2 : 6

Hence, time taken by A = 72/6
 = 12 minutes.

Question: A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes, respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

Solution:
Part filled by (A + B) in 1 minute = 1/60 + 1/40
= (2 + 3)/120
= 1/24

(A + B) will take half of total time= (x/2)​× (1/24)
The rest half will be filled by B only in half of total time = (x/2)​ × (1/40)

Now
x/48 + x/80 = 1
(5x + 3x)/240 = 1
8x/240 = 1
x/30 = 1
x = 30 

Question: Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, in another race of same type runner B finished 8 metres ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is:

Solution:
Let A finish the race of x metres
B finish the race of = x - 12 meters.
C finish the race of = x - 18 - - - - - - - - (1)
In another race of B & C
B finish race of = x meters.
C finish race of = x - 8 - - - - - - - - (2)
Ratio of speeds of B & C
(x - 12)/(x - 18) = x/(x - 8)
⇒ (x - 12)(x - 8) = x(x -18)
⇒ x² - 12x - 8x + 96 = x² - 18x
⇒ x^{2 -} 20x + 96 = x² - 18x
⇒ 96 = 2x
∴ x = 48 metres.

∴ The length of the race is 48 meters.

Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

Solution:
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10)
= 3(2 + 3 + 6)/60
= 3(11/60)
= 11/20

Part filled by C in 3 minutes = 3/10

∴ Required ratio = (3/10) × (20/11)
= 6/11

Question: The capacity of containing water of a tank is 8000 litres. The length of the tank is 2.56 metres and breadth is 1.25 metres. What is the depth of the tank?

Question: A man travels the distance of his journey 3/4 by bus, 1/6 by rickshaw and remaining 2 km on foot. The total distance travelled by the man is:

Solution:
Let the man travels 1 unit distance
So, remaining distance
= 1 - (1/6 + 3/4)
= 1 - 22/24
=1/12

∵ 1/12 unit = 2 km
So, 1 unit = 24 km.

Question: Each wheel of a car is making 5 revolutions per second. If the diameter of a wheel is 84 cm, then the speed of the car in cm/sec would be:

Solution:
Given,
the diameter of a wheel is 84 cm
the radius of a wheel is, r = 84/2 = 42

Circumference of the circle = 2πr
= 2 × (22/7)× 42
= 264 cm
Distance cover in 1 sec = 264 × 5
= 1320 cm/sec

Question: A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time to fill the cistern completely?

Solution:
Time is taken to fill half of the tank = (1/2) × 16 = 8 hrs
In 1 hour pipe can fill = 1/16 part filled by 4 pipes in1 hour = 4 × (1/16) = 1/4 part
So, remaining half part = 4 × (1/2) = 2 hours
∴ Total time = 8 +  2 = 10 hours.

Question: The distance between places A and B is 999 km. An express train leaves place A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hour 20 minutes. It reaches B at:

Solution:
Time will be taken by train if it does not stop = Distance/Speed
= 999 km/55.5 km/hr
Without stop = 18 hr

But if stops on the way for 1 hour 20 minutes before reaching B.
Total time = 18 hr + 1 hr 20 min
= 19 hour 20 minutes

Reaching time at B = 6 am + 19 hr 20 min
= 1.20 am

Question: 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:

Solution:
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

Question: A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

Solution:
Time taken in walking both the ways = 7 hours 45 minutes - - - - - - - - (1)
Time taken in walking one way and riding back = 6 hours 15 minutes - - - - - - - - (2)

By the equation (2) × 2 - (1), we have,
Time taken by the man in riding both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes.

Question: 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?

Solution:
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
∴ x = 60 km/hr

Required distance = 8 × 60
= 480 km.

Question: A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

Solution:
Let the total capacity of the tank is 30 units.
The efficiency of Leakage(Pipe A) will be 30/10 = 3
And the efficiency of the leakage (Pipe A) and another Pipe (B) which is filling the tank will be 30/15 = 2

Pipe A is emptying at 3 units/hr and when filling pipe B started then the emptying rate will come down to 2 units/hr.
∴ Filling Pipe B efficiency is 3 - 2 = 1 unit/hr
Pipe B will be fill the tank in 30/1 = 30 hrs.

The filling rate of Pipe B per minute is 4 litter
∴ Total Capacity of tank will be = (4 × 60) × 30 = 7200 litters.

Question: A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

Solution:
We know,
Average speed = Total distance/Total time
= (50 + 40 + 90)/(2 + 2 + 6) km/hr
= 180/10 km/hr
= 18 km/hr.