ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A runner can complete a 750 m race in two and a half minutes. What is the speed of runner in km/hr?

Solution:
We are given that the first runner can complete a 750 m race in 2 minutes and 30 seconds or 150 seconds. 
∴ Speed of the first runner = 750/150 = 5m/sec 

We convert this speed to km/hr by multiplying it by 18/5. 
Speed of the first runner = (5 × 18)/5 = 18 km/hr

Question: An outgoing pipe is attached to a tank that can empty it in 20 hours. An ingoing pipe is connected to the tank that can fill it in 8 hours. How much time will it take to fill the half-full tank?

Solution: 
ingoing pipe in one hour can fill = 1/8
outgoing pipe in one hour can empty = 1/20

in one hour total fill up = 1/8 - 1/20 = 3/40

to fill half the tank it will take = 40/6 = 20/3 hours.

Question: A man takes 50 minutes to cover a certain distance at a speed of 6km/hr. If he walks with a speed of 10km/hr, he covers the same distance in -

Solution: 
distance = speed × time
= (6 × 50/60)
= 5km

time = distance/ speed
= 5/10
= 1/2 hour
= 30 minutes

Question: A car travels from point A to B at 60km/hr and from point B to A at 90km/hr. What is the average speed of the car?

Solution: 
Let the distance from A to B be x,
time of first travel = x/60 hr
time of second travel = x/90 hr

average = 2x/{(x/60) + (x/90)}
= 72km/hr

Question: A boy walked 20 minutes at 3km/hr and ran 20 minutes at 15km/hr. The total distance covered by the boy is - 

Solution:
first 20 minutes he covered
= 3 × 20/60 km
= 1km

in the second 20 minutes, he covered 
= 15 × 20/60 km
= 5km

total distance = 1 + 5 = 6km

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 12 hours. Another pipe alone can fill two tanks in - 

Solution: 
let the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/12 + 1/X
= (X + 12)/12X

Atq,
12X/(X + 12) = 6
x = 12 hours.

to fill two tanks it will take = 24 hours

Question: A car covers the first 30km in 15 minutes and the second 30km in 10 minutes. Between the two actions, the car stopped for 5 minutes for fuel. What is the average speed of the car?

Solution: 
total distance = 30 + 30 = 60km
total time = 30 minutes = 1/2 hour

average = 60/(1/2) = 120km/hr.

Question: Rakib is walking at 5m/s. Tanvir was 200m behind Rakib and started walking at 7m/s towards Rakib. After how much time will Tanvir catch Rakib?

Solution:
let after t seconds Tanvir will catch Rakib.
in t seconds,
Rakib will cover = 5t m 
Tanvir will cover = 7t m

∴ 7t = 5t + 200
2t = 200
t = 100 seconds

Question: A train is passing a platform at 20m/s and a man is walking at 2m/s in the opposite direction. It took 10 sec for the train to cross the man. What is the length of the train?

Solution: 
as they are going opposite,
resultant speed is = (20 + 2) m/s
= 22 m/s

the length of the train is = 22 × 10 = 220m

Question: The speed of A and B are in the ratio 3 : 5. A takes 30 minutes more than B to reach a destination. Time in which A reaches the destination?

Solution: 
speed ratio = 3 : 5
time ratio = 5 : 3
∴ 5x - 3x = 30
x = 15

time of A = 5 × 15 = 75 minutes
= 1 hour 15 minutes.

Question: In a race of 1000m, A can beat B by 100m. In a 400m, B beats C by 40m. In a race of 500m. A will beat C by-

Solution:
While A covers 1000 B covers 900
while A covers 500 B covers 450m

While B covers 400, C covers 360m
While B covers 450, C covers (360 × 450)/400 = 405m

∴ in a 500m race A will beat C  by = (500 - 405) = 95m

Question: A tank with a capacity of T liters is empty. If water flows into the tank from pipe X at the rate of x liters per minute and water is pumped out by Y at the rate of y liters per minute and x>y, then in how many minutes will the tank be filled?

Solution:
per minute fill up = x - y liters

∴ total time to fill the tank is = T/(x - y) 

Question: A monkey climbs a 40m high pole. In the first minute, he climbs 3m and slips down 1m in the next minute. How much time is required by it to reach the top?

Solution: 
in two minutes,
total distance covered by the monkey is = 3 - 1 = 2m
in 1 minute = 2/2 = 1m

in 36 minutes it will cover = 36m
in the 37th minute, it will go up to = 36 +3 = 39m
in the 38th minute, it will fall 1m ad thus covers = 39 - 1 = 38m

the rest of the 2m of total 40m will be climbed in 1 minute.
thus total time to reach the peak is = 38 + 1 = 39 minutes.

Question: A is faster than B. A and B each walk 24km. The sum of their speeds is 7km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to - 

Solution:
Let, A's speed be = x km/hr
B's speed is = (7 - x) km/hr

ATQ,
24/x + 24/(7 - x) = 14
or, {24(7 - x) + 24x}/{x(7 - x) = 14
or, 24(7 - x) + 24x = 14x(7 - x)
or, 14x² - 98x + 168 = 0
or, x² - 7x + 12 = 0
or, (x - 3)(x - 4) = 0
∴ x = 3 or, x = 4

as A's speed is greater than B. 
so, x = 4

Question: In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is -

Solution: 
According to the question,
When B runs 200 m meters, A runs 190 meters;
Hence, when B runs 180 meters,
A runs = (190×180)/200
= 171 meters

When C runs 200m, B runs 180 meters.
Hence,
C will give a start to A by = 200 - 171
= 29 meters

Question: How long will it take for two pipes to fill a tank together when they can fill it alone in 14 hours and 21 hours respectively?

Solution:
together in one hour they can fill = 1/14 + 1/21 = 5/42

so, the total time to fill the tank is = 42/5 hours =  8.4 hours

Question: 15 buckets of water fill a tank when the capacity of each bucket is 16 liters. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 12 liters?

Solution: 
total capacity of the tank is = (15 × 16) = 240 liters.

total buckets of 12 liters = 240/12 = 20 buckets

Question: An individual is cycling at a speed of 25 km per hour. He catches his predecessor, who started earlier, in two hours. What is the speed of his predecessor, who started three hours earlier?

Solution: 
The distance covered in two hours,
= 2 × 25 = 50 km
Time taken by first individual = (3h + 2h) = 5h
Then, the speed of the predecessor,
= 50/5 = 10 km/hr

Question: Sayed covers 20 miles in 40 minutes. What is his speed in km/hr?

Solution:
We know that,
1 mile = 1.61km
20 miles = (20 × 1.61)km
= 32.2 km

time = 40 minutes = 40/60 = 2/3 hour

speed = 32.2/(2/3) km/hr
= 48.3 km/hr

Question: Tap P fills a tank in 4 hours whereas tap Q empties the tank in 24 hours. P and Q are opened alternately for 1 hour each. Every 2 hours the level of water is found to increase by 0.5m. The depth of the tank is - 

Solution: 
let, the depth of the tank is = h

in two hours total fill-up = 1/4 - 1/24
= 5/24

∴ (5/24)h = 0.5
h = 2.4m

Question: Two boats A and B start towards each other from two places, 108 km apart. The speeds of boats A and B in still water are 12 km/h and 15 km/h respectively. If A proceeds down and B up the stream, they will meet after:

Solution: 
Let the speed of the stream be x km/h and both the boats meet after t hour.

A's speed is = 12 + x
B's speed is = 15 - x

According to the question,
(12 + x) × t + (15 - x) × t = 108
Or, 12t + 15t = 108
Or, 27t = 108
∴ t = 4 hours

Question: A motorcyclist completes a certain journey in 5 hours. He covers one-third of the distance at 60 km/hr and the rest at 80km/hr. the length of the trip is - 

Solution: 
Let the total length of the trip be = x km
one-third or x/3 distance covered at 60km/hr.
time = (x/3)/60 hr

Two-thirds of the distance covered at 80km/hr
time = (2x/3)/80 hr

ATQ,
(x/3)/60 + (2x/3)/80 = 5
or, (2x + 3x)/360 = 5
or, 5x/360 = 5
∴ x = 360 km

Question: Water flows through a cylindrical pipe of an internal diameter of 7cm at the rate of 5m/s. The time, in minutes, the pipe would take to fill an empty rectangular tank of 4m × 3m × 2.31m is - 

Solution: 
the total volume of the tank is = 400 × 300 × 231 cc
total water flow per second through the pipe is = πr²h
= (22/7) × (7/2)² × 500

∴ total time = (400 × 300 × 231)/{(22/7) × (7/2)² × 500}
= (400 × 300 × 231 × 4 × 7)/(22 × 49 × 500)
= 1440 s 
= 24 min