ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A, B, and C completed a work costing Tk 2250. A worked for 6 days, B for 4 days, and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much will A receive?

Solution:
Let the daily wages of A, B, and C be Tk 5x, 6x, and 4x respectively.

Then, ratio of their amounts
=(5x × 6) : (6x × 4) : (4x × 9)
= 30 : 24 : 36
= 5 : 4 : 6

∴A's amount = 2250 × (5/15) = 750 Tk

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is - 

Solution:
Let A alone takes x days 
and B alone takes 3x days to complete the job.

ATQ,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A alone takes 20 days and B alone takes 3 × 20 = 60 days to complete the job.

(A + B)'s 1 days work = (1/20 + 1/60) = 1/15 part

∴ A and B together can do the work in 15 days.

Question: 3 pumps, working 12 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
3 pumps need 2 days by working 12 hours
1 pump needs 1 day by working 12 × 3 × 2 hours
4 pumps need 1 day by working (12 × 3 × 2)/4 hours
= 18 hours

Question: If 9 examiners can examine a certain number of answer books in 12 days by working 5 hours a day; for how many hours a day would 4 examiners have to work in order to examine twice the number of answer books in 27 days?

Solution:
9 examiners  need 12 days by working 5 hours
1 examiner needs 1 day by working 5 × 9 × 12 hours
4 examiners  need 27 days by working (5 × 9 × 12)/(4 × 27) hours
= 5 hours

So, twice the work need twice time.
∴ So, the answer = (5 ×  2) = 10 hours

Question: If 6 persons working 8 hours a day earn Tk 9600 per week, then 9 persons working 6 hours a day will earn per week?

Solution:
Earning of 6 × 8 = 48 hours is 9600 Tk
Earning of 1 hour is 9600/48 Tk
Earning of 9 × 6 = 54 hours is  (9600 × 54)/48 Tk
= 10800 Tk

Question: A man completes 2/3 of a job in 12 days. At this rate, how many more days will it take him to finish the job?

Solution:
Rest part of job = 1 - 2/3 = 1/3

2/3 of the work done in 12 days
1 of the work done in (12 × 3)/2 days
1/3 of the work done in (12 × 3)/(2 × 3) days
= 6 days

Question: A garrison of 400 men had food for 27 days. After 3 days a reinforcement of 200 men arrived. For how many more days will the remaining food last now?

Solution:
After 3 days, food having for = 27 - 3 = 24 days
After arriving 200 men, total men = 400 + 200 = 600 men

400 men can eat the food for 24 days
1 man can eat the food for 24 × 400 days
600 men can eat the food for (24 × 400)/600 days
= 16 days

Question: A fort had food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is -

Solution:
After 10 days, food having for = 45 - 10 = 35 days
After 25 men left, total = 150 - 25 = 125 men

150 men can eat food for 35 days
1 man can eat food for (35 × 150) days
125 men can eat food for (35 × 150)/125 days
= 42 days

Question: A canteen requires 420 bananas for a week. Totally, how many bananas will it require for the months of January, February, and March in 2024?

Solution:
January = 31 days
February = 29 days
March = 31 days

Total = 31 + 29 +31 = 91 days

In 7 days the canteen requires 420 bananas
In 1 day the canteen requires 420/7 bananas
In 91 days the canteen requires (420 × 91)/7 bananas
= 5460 bananas

Question: Some persons can do a piece of work in 24 days. Two times the number of such persons will do half of that work in -

Solution:
Let the initial workers be x
So, workers for 2nd time = 2x

x persons can complete 1 part in 24 days
1 person can complete 1 part in 24x days
2x persons can complete 1/2 part in 24x/(2x × 2) days
= 6 days

Question: 5 mat-weavers can weave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?

Solution:
5 mat-weavers in 5 days can weave 5 mats
1 mat-weaver in 1 day can weave 5/(5 × 5) mats
10 mat-weavers in 10 days can weave (5 × 10 × 10)/(5 × 5) mats
= 20 mats

Question: If a quarter kg of potato costs 20 Tk, how much Tk will 200 gm cost?

Solution:
A quarter of 1 kg = 1/4 kg
200 gram = 200/1000 = 1/5 kg

1/4 kg of potato's cost is 20 Tk
1 kg of potato's cost is 20 × 4 Tk
1/5 kg of potato's cost is (20 × 4)/5 Tk
= 16 Tk

Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?

Solution:
B's 1 day's work = 1/12 - 1/20 = 1/30
If B does the work half a day, then he will do = 1/30 ÷ 2 = 1/60

Now, (A + B)'s 1 day's work = 1/20 + 1/60 = 1/15

So, A and B together will complete the work in 15 days.

Question: A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -

Solution:
Let, A, B, and C take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively

Now, 
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, A takes = 6 × 3 = 18 days

Question: A, B, and C can complete a piece of work in 8, 12, and 24 days respectively. Working together, they will complete the same work in -

Solution:
(A + B + C)'s 1 days work = 1/8 + 1/12 + 1/24 
= (3 + 2 + 1)/24
= 6/24
= 1/4

A, B, and C together can complete the work in = 4 days

Question: A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

Solution:
A completes one job in 12 days.
Hence the fraction of the job completed by A in 1 day =1/12

Since B is 60% more efficient than A,
Hence the fraction of the total job completed by B on one day =1/12 + 1/12 × (60/100)
= 1/12 + 1/20
= (5 + 3)/60
= 8/60
= 2/15

B can finish the job in 15/2 = 7.5 days

Question: A can do a piece of work in 24 days. When he had worked for 4 days, B joined him. If the work was finished in 16 days, B can alone finish that work is -

Solution:
A's 1 day's work = 1/24 part
A's 16 day's work = 16/24 part
= 2/3 part

Remaining work  = 1 - 2/3 = 1/3 part

1/3 part work done by B in 16 - 4 = 12 days
1 part work done by B in 12 × 3 = 36 days

লাইভ পরীক্ষার প্রশ্নে ভুল ছিল। তাই উত্তর তুলে দেয়া হয়েছে।

প্রশ্নটি হবে -
Question: A can do 1/4 of a work in 10 days, B can do 40% of the work in 40 days, and C can do 1/3 of the work in 13 days. Who will complete the work first?

Solution:
Whole work will be done by A in (10 × 4) = 40 days
Whole work will be done by B in (40 × 100/40) = 100 days
Whole work will be done by C in (13 × 3) = 39 days

সে অনুসারে সঠিক উত্তর হতো - গ) C

Question: 5 men and 2 boys working together can do four times as much as work as a man and a boy. Working capacities of a man and a boy are in the ratio -

Solution:
Let, 1 man's 1 days's work = x
and 1 boy's 1 day's work = y

ATQ,
5x + 2y = 4(x + y)
⇒ 5x + 2y = 4x + 4y
⇒ x = 2y
⇒ x/y = 2/1
⇒ x : y = 2 : 1

Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many days men will be catered to with the remaining meal?

Solution:
Camp has = 200 children
Already have taken meal  = 150 children

Remaining children to take meal = 200 - 150 = 50 children

the camp has meal for 200 children = 120 men
the camp has meal for 1 children = 120/200 men
the camp has meal for 50 children = (120 × 50)/200 men
= 30 men