ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: Kawser travelled 4/7 as many miles on foot as by water and 2/5 as many miles on horseback as by water. If he covered total of 3036 miles, how many miles did he travel on foot?

Solution:
Suppose Kawser travelled x miles by water, 4x/7 miles on foot and 2x/5 miles on horseback.

ATQ,
x + 4x/7 + 2x/5 = 3036
⇒ 69x/35 = 3036
⇒ x = (3036 × 35)/69
∴ x = 1540

∴ Distance travelled on foot :
=(4 ×1540)/7 miles
= 880 miles

Question: A train takes 18 seconds to pass completely through a station 162m long and 15 seconds through another station 120m long. The length of the train is-

Solution:
ট্রেনটি 18 সেকেন্ডে অতিক্রম করে 162 মিটার + ট্রেনের দৈর্ঘ্য
ট্রেনটি 15 সেকেন্ডে অতিক্রম করে 120 মিটার + ট্রেনের দৈর্ঘ্য
ট্রেনটি 3 সেকেন্ডে অতিক্রম করে = 42 মিটার
ট্রেনটি 1 সেকেন্ডে অতিক্রম করে = 42/3 মিটার
ট্রেনটি 15 সেকেন্ডে অতিক্রম করে = (42 × 15)/3 মিটার
= 210 মিটার

∴ ট্রেনটির দৈর্ঘ্য = (210 - 120) মিটার = 90 মিটার।

Question: Niloy walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles?

Solution:
Niloy needs time = 50/10 = 5 hours
= (5 × 60)
= 300 minutes

He will also rest 4 times after 10, 20, 30 and 40 miles
Total resting time = 4 × 6 = 24 minutes.

Total time = 300 + 24 = 324 minutes

Question: A man swimming in a stream which flows 3/2 km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

Solution:
Let, speed upstream = x km/hr
speed downstream = 2x km/hr
Speed of stream = (2x - x)/2 = x/2 km/hr.

ATQ,
x/2 = 3/2
∴ x = 3

speed upstream = 3 km/hr
Speed downstream = 2 × 3 = 6 km/hr

Hence, rate of swimming = (3 + 6)/2 = 4.5 km/hr

Question: A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is :

Solution:
Let, the distance travelled by a car be x km
First x/3 km distance cover at a speed of 10 km/hr
Second x/3 km distance cover at speed = 20 km/hr
Third x/3 km distance cover at speed = 60 km/hr

According to the question,
Total time = x/(3 × 10) + x/(3 × 20) + x/(3 × 60)
= x/30 + x/60 + x/180
= (6x + 3x + x)/180
= 10x/180
= x/18

Average speed = (x × 18)/x km/hr = 18 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:
Let C's speed = x km/hr
Then, B's speed = 3x km/hr
And A's speed = 6x km/hr
∴ Ratio of speeds of A, B, C
= 6x : 3x : x
= 6 : 3 : 1
Ratio of times taken
= 1/6 : 1/3 : 1
= 1 : 2 : 6

If C takes 6 minutes, then A takes 1 minute
If C takes 72 minutes, then A takes (1/6) × 72 min = 12 min

Question: Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Solution: 
Let the speed of the second lady be x km/hr
Then, speed of first lady = (x + 2) km/hr

ATQ,
24/x - 24/(x + 2) = 1
⇒ x(x + 2) = 48
⇒ x² + 2x - 48 = 0
⇒ x² + 8x - 6x - 48 = 0
⇒ x(x + 8) - 6(x + 8) = 0
⇒ (x + 8)(x - 6) = 0
⇒ x = 6

Hence, speed of first lady = 8 km/hr
The speed of the second lady = 6 km/hr

Question: A Boat takes a total 10 hours for traveling downstream from point A to point B and coming back point C which is somewhere between A and B. The speed of the Boat in still water is 9 km/hr and rate of stream is 3 km/hr, then what is the distance between A and B if the ratio of distance between A to C and distance between B to C is 2 : 1?

Solution:

Let, the distance between B to C = x
the distance between A to C = 2x
the distance between A to B = 3x

ATQ,
3x/12 + x/6 = 10
⇒ (3x + 2x)/12 = 10
⇒ 5x = 120
∴ x = 24

∴ The distance between A to B = 3 × 24 = 72 km

Question: The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be - 

Solution:
Speed of train relative to man
= (44 - 8) kmph
= 36 kmph
= (36 × 5)/18m/sec
= 10 m/sec

∴ Time taken to pass the man
= 180/10 sec
= 18 sec

Question: Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more then the first. The distance between A and B is :

Solution:
At the time of meeting, let the distance travelled by the first train be x km.
Then, discount covered by the second train = (x + 120) km

ATQ,
x/50 = (x + 120)/60
⇒ 60x = 50(x + 120)
⇒ 60x - 50x = 6000
⇒ 10x = 6000
∴ x = 600 

So, distance between A and B = (x + x + 120) km
= (600 + 600 + 120) km
= 1320 km

Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Solution: 
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার 

ট্রেনটি 240 মিটার অতিক্রম করতে সময় নেয় = 24 সেকেন্ড 
ট্রেনটি1 মিটার অতিক্রম করতে সময় নেয় = 24/240 সেকেন্ড 
ট্রেনটি 890 মিটার অতিক্রম করতে সময় নেয় = (24 × 890)/240 সেকেন্ড 
= 89 সেকেন্ড

Question: Two trains of equal length are running on parallel lines in the same direction at 50 km/hr and 60 km/hr. The faster train passes the slower train in 72 seconds. The length of each train is:

Solution:
Let the length of each train be x metres.
Then, distance covered = 2x metres.

Relative speed = (60 - 50) km/hr
= 10 km/hr
= (10 × 1000)/3600 m/s
= 25/9 m/s 

Now,
2x/72 = 25/9
⇒ 18x = 1800
∴ x = 100

Question: The ratio between the speed of a bus and train is 15 : 27 respectively. Also, a car covered a distance of 720 km in 9 hours. The speed of the Bus is three-fourths the speed of the car. How much distance will the train cover in 7 hours?

Solution:
Ratio of speed of Bus and Train = 15 : 27
Let speed of the bus is 15x and Speed of the Train is 27x.
Car Covered 720 km in 9 hours.
So, Speed of the Car = 720/9 = 80 kmph

Given, Speed of the bus is 3/4 of Car,
So speed of the Bus = (80 × 3)/4 = 60 kmph

Thus, 15x = 60
∴ x = 4

So, Speed of the train = 27x = 27 × 4 = 108 kmph.
Hence, Train will cover distance in 7 hours,
= 108 × 7
= 756 km

Question: A man can row upstream at 24km/hr and downstream at 16km/hr. The man rowing speed in still water is?

Solution:
Let, x = downstream speed and y = upstream speed
We know,
Speed of boat in still water = (x + y)/2
∴ Boat's speed = (24 + 16)/2 = 40/2 = 20 km/hr.

Question: An inspector notices a thief from a distance of 200 meters after this thief starts running and the inspector chases him. The inspector and the thief run at the speed of 11 km/hr and 10 km/hr respectively. The distance between them after 6 minutes is?

Solution:
চোর ও ইন্সপেক্টরের আপেক্ষিক গতি = (11 - 10) km/hr
= 1 km/hr
6 মিনিটে অতিক্রম করে = {(1/60) × 6}km
= 1/10 km
= 100 m

∴ চোর ও ইন্সপেক্টরের মধ্যবর্তী  দূরত্ব = (200 - 100) m
= 100 m

Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in  6 seconds. The speed of the second train is _____

Solution:
Distance covered = (108 + 112)
= 220 meter.
Time = 6 seconds.

Relative speed = 220/6 = 110/3 m/s.
= (110 × 3600)/(3 × 1000) km/hr
= 132 km/hr.

Now,
50 + Speed of second train = 132 km/hr.
∴ Speed of second train = (132 - 50) km/hr.
= 82 km/hr.

Question: A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the downstream speed in km/hr?

Solution:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr

ATQ,
30/(15 + x) + 30/(15 - x) = 4(1/2)
Or, 900/(225 - x²) = 9/2
Or, 9x² = 225
Or, x²  = 25
∴ x = 5 km/hr

∴ The downstream speed = (15 + 5) km/hr = 20 km/hr

Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is -

Solution:
Let length of the train be x m and speed of the train is s kmph.
Speed, s = (x + 800)/100 . . . . . (i)
Speed, s = (x + 400)/60. . . . . (ii) 

Equating equation (i) and (ii),
we get,
(x + 800)/100 = (x + 400)/60
Or, (x + 800)/5 = (x + 400)/3
Or, 5x + 2000 = 3x + 2400
Or, 2x = 400
∴ x = 200m

∴ The length of the train is 200 meters.