ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?

Solution:
The work rate of X is 1/12 (since X can complete the work in 12 days).
The work rate of Y is 1/18 (since Y can complete the work in 18 days).
In 3 days they complete = 3{(1/12) + (1/18)}
= 3 × (5/36)
= 5/12

Then the fraction of work that is left is = 1 - (5/12)
= (12 - 5)/12
= 7/12

Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

Solution:
One day's work of A, B, and C = (1/24) + (1/30) + (1/40) = 1/10.
C leaves four days before the work is completed, which means only A and B work during the last four days.
The work done by A and B together in the last four days is = 4 {(1/24) + (1/30)} = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.
Number of days required for this initial work = 7 days.
Thus, the total numbers of days required = 4 + 7 = 11 days.

Question: P can build a wall in 24 days and Q can do it in 20 days. With help of R, they completed the work in 6 days. Find in how many days R alone can do the work.

Solution:
P can do 1/24 part per day
Q can do 1/20 part per day
R can do per day = (1/6) - {(1/24) + (1/20)}
= (1/6) - (11/120)
= (20/120) - (11/120)
= 3/40
Time taken by R alone = 40/3 days

Question: Sarah finishes 60% of a painting in 12 days. She then asks David to help and together they complete the remaining work in 4 days. How many days would David take to complete the whole painting alone?

Solution:
Sarah does 60% or 3/5 work in 12 days
in one day, she does 1/20 work
in 4 days, she does 1/5 work
work remaining = (2/5) - (1/5)
= 1/5 work
David does 1/5 parts in 4 days
he will complete the work in 20 days

Question: If Machine X can produce 1,000 bolts in 4 hours and Machine Y can produce 1,000 bolts in 5 hours, in how many hours can Machines X and Y, working together at these constant rates, produce 1,000 bolts?

Solution:
Machine X can produce 100 bolts in 4 hrs.
In an hour X can produce 1000/4 = 250 bolts 

Machine Y can produce 1000 bolts in 5 hrs.
In an hour Y can produce 1000/5 = 200 bolts 

Together they can produce 250 + 200 = 450 bolts in an hour.
They will produce 1000 bolts in 1000/450 hours.
= 20/9 hours.

Question: 5 machines, working 6 hours a day, can produce 300 units in 3 days. How many hours a day must 10 machines work to produce 300 units in 1 day?

Solution:
5 machines, working 6 hours a day, can produce 300 units in 3 days
Formula used: M1 × T1 = M2 × T2
Where M1 and M2 is machines and T1 and T2 is time

Let H hours be the number of hours required
Applying the above formula
⇒ 5 × 6 × 3 = 10 × 1 × H
⇒ 90 = 10H
⇒ H = 90/10
⇒ H = 9 hours
∴ 10 machines need to work 9 hours to complete the work in 1 day.

If the cost of p metres of wire is Tk. d, then what is the cost of q metres of wire at the same rate (in Tk)?

Solution:
Cost of p metres = Tk. d
Cost of 1 metre = Tk. d/p
Cost of q metres = Tk. dq/p

Question:  A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Tk. 3000 for the whole work, the daily wages of B and C together is:

Solution:
Part of work done by A= 1/10 × 5 ⇒ 1/2
Part of work done by B = 1/15 × 5 ⇒ 1/3
Part of work done by C = 1 - (1/2 + 1/3)
⇒ 1 - 5/6
⇒ 1/6
∴ (A’s share) : (B’s share) : (C’s share) = 1/2 : 1/3 : 1/6
⇒ 3 : 2 : 1

A’s share = 3/6 × 3000 ⇒Tk. 1500
B’s share = 2/6 × 3000 ⇒Tk. 1000
C’s share = 1/6 × 3000 ⇒Tk. 500

A’s daily wages = 1500/5 ⇒ Tk. 300
B’s daily wages = 1000/5 ⇒ Tk. 200
C’s daily wages = 500/2 ⇒ Tk. 250
Daily wages of Y and Z = (200 + 250) ⇒Tk. 450

The daily wages of B and C together is Tk. 450.

Question: A fort has enough food for 180 soldiers for 60 days. After 20 days, 60 soldiers leave. For how many more days will the remaining food last-

Solution:
After 20 days: 180 soldiers had food for 40 days. Suppose 120 soldiers had food for x days.
Now, fewer soldiers, more days (Indirect Proportion):
120 : 180 : : 40 : x
⇒ 120/180 = 40/x
⇒ 120x = 180 × 40
⇒ x = (180 × 40)/120
∴ x = 60

Question: Rakib and Kabila are working on an assignment. Rakib takes 6 hours to type 32 pages on a computer, while Kabila takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 220 pages?

Solution:
Number of pages typed by Rakib in 1 hour = 32/6 = 16/3
Number of pages typed by Kabila in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3

Therefore Time taken by both to type 220 pages = 220 × (3/40) hours
= 33/4 hours
= 16.5 hours
= 16 hour 30 minutes

Question: A man completes 5/8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

Solution:
Work done = 5/8
Balance work = 1 - (5/8) = 3/8

Let the required number of days be x
Then,
(5/8) : (3/8) :: 10 : x
⇒ (5/8) × x = (3/8) × 10
⇒ x = (3/8) × 10 × (8/5)
∴ x = 6

Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 4 days. B can do the work alone in-

Solution:
Suppose A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then,
1/x + 2/x + 3/x = 1/4
⇒ 6/x = 1/4
⇒ x/6 = 2
∴ x = 24

So, B takes (24/2) = 12 days to finish the work.

Question: In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk?

Solution:
50 cows can eat 50 bags of husk in 50 days
1 cow can eat 1 bag of husk in (50 × 50)/50 days
= 50 days

Question: A wheel that has 12 cogs is meshed with a larger wheel of 24 cogs. If the smaller wheel has made 44 revolutions, then find the number of revolutions made by the larger wheel.

Solution:
As number of cogs increase, the revolutions made decrease. Hence, this is a problem related to indirect proportion.
Let the number of wheels be x.
More cogs (↑),Less revolutions (↓)

24 : 12 : : 44 : x
⇒ 24 × x = 12 × 44
⇒ x = (12 × 44)/24
∴ x = 22

Question: James hired some workers to build his house in 20 days. But on the day of starting of the construction, 12 men did not come. Rest of the people then built the entire house in 32 days. How many workers had he initially hired?

Solution:
Initially hired workers = x
Total work = x × 20 (man-days)
After 12 workers didn't come, Remaining workers = x - 12
Total work = (x - 12) × 32 (man-days)

ATQ,
x × 20 = (x - 12) × 32
⇒ 20x = 32x - 384
⇒ 12x = 384
∴ x = 32

Question: 35 men can make 70 toys in 8 days by working 8 hours a day. How many days will 56 men need to make 84 toys by working 12 hours every day?

Solution:
Total man-hours for 70 toys:
35 × 8 × 8 = 2240 man-hours
So, Man-hours per toy = 2240/70 = 32

Total man-hours for 84 toys:
84 ×  32 = 2688 man-hours
Total man-hours per day for 56 men working 12 hours:
56 × 12 = 672 man-hours/day

∴ Time to complete work = 2688/672 = 4 days

Question: If the number of workers is doubled, how many times more time will be required to complete the task?

Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর দিগুণ = 2x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
২x জন কাজটি করে = xn/২x
= n/২ সময়ে বা ১/২ সময়ে।

Question: In a camp, there is a meal for 240 men or 400 children. If 300 children have taken the meal, how many men will be catered to with remaining meal?

Solution:
Camp has = 400 children
Already have taken meal = 300 children

Remaining children to take meal = 400 - 300 = 100 children

the camp has meal for 400 children = 240 men
the camp has meal for 1 children = 240/400 men
the camp has meal for 100 children = (240 × 100)/400 men
= 60 men

Question: The price of 357 apples is Tk. 1517.25. Find the approximate price of 49 dozens of such apples?

Solution:
1 dozen = 12 pcs
49 dozens = 49 × 12 = 588 apples

Now,
357 apples = 1517.25 Tk.
∴ 1 apple = 1517.25/357 Tk.
∴ 588 apples = (1517.25 × 588)/357 Tk.
= 2499 Tk.

Question: A canteen requires 553 liters of water for a week. Totally, how many liters will it require for the months of May, June, July?

Solution:
একদিনে পানি লাগে = 553/7 = 79 লিটার
May, June, July মাসে মোট দিন = (31 + 30 + 31) = 92 দিন।

∴ মোট পানি লাগবে = (92 × 79) = 7268 লিটার

Question: A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job?

Solution:
Let the team take x days to finish 360 pieces
Then, number of pieces made each day = 360/x
More number of pieces per day, Less days (Indirect proportion)

Question: If half kg of potatoes costs 80 paise, how many paise will 300 gm cost?

Solution:
Let the required weight be x kg. Less weight, less cost (Direct Proportion)

500 : 300 : : 80 : x
⇒ 500/300 = 80/x
⇒ 500x = 24000
⇒ x = 24000/500
∴ x = 48.
The cost of 300 gm of potatoes will be 48 paise.