ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: 42 binders can bind 1400 books in 15 days. How many binders will be required to bind 800 books in 20 days?

Solution:
In 15 days 1400 books can be bound by 42 binders
In 1 day 1 book can be bound by (42 × 15)/1400 binders
In 20 days 800 books can be bound by (42 × 15 × 800)/(1400 × 20) binders
= 18 binders

Question: Four gardeners with four grassmowers mow 400 sq. m of ground in 4 hours. How long would it take for eight gardeners with eight grass mowers to mow 800 sq. m of the ground?

Solution:
Since each gardener would work with one grassmower,
So, we shall consider 1 gardener and 1 grass mower as one unit.
Let the required time be x hours

ATQ,
8 × 400 × x = 4 × 800 × 4
⇒ x = (4 × 800 × 4)/(8 × 400)
∴ x = 4 hours

Question: In a camp of soldiers there was a stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the leftover food last for the remaining soldiers?

Solution:
Let, the remaining food last for x days
4000 soldiers had provision for 160 days
3200 soldiers had provision for x days

ATQ,
3200 : 4000 = 160 : x
⇒ 3200x = 4000 × 160
⇒ x = (4000 × 160)/3200
∴ x = 200

The remaining food last for 200 days.

Question: M does one-third as much work as N in one-fourth of the time. If together they take 12 days to complete a work, how much time shall N alone take to do it?

Solution:
Let N takes x days to do the work.
M takes 1/4 of x time to do 1/3 of the work.
∴ The work will be done by M in (x/4) × 3 days
= 3x/4 

ATQ,
1/x + 4/3x = 1/12
⇒ 7/3x = 1/12
⇒ 3x = 84
∴ x = 28

∴ N alone will take 28 days.

Question: A canteen requires 672 bananas for a week. Totally, how many bananas will it require for the months of March, April and May?

Solution:
Total number of days = (31 + 30 + 31) = 92
Let the number of bananas be x

ATQ,
7/92 = 672/x
⇒ 7x = 92 × 672
⇒ x = (92 × 672)/7
∴  x = 8832

Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Solution: 
C's 1 day's work = 1/3 - (1/6 + 1/8)
= (1/3) - (7/24)
= 1/24

A's wages: B's wages: C's wages = 1/6 : 1/8 : 1/24
= 4 : 3 : 1.

C's share (for 3 days) = Tk. 3 × 1/24 × 3200 = Tk. 400.

Question: If 20 boys or 10 men can make 20 cricket bats in 10 days, then how many cricket bats will be made by 4 boys and 8 men in 20 days?

Solution:
Here, 
10 men = 20 boys
8 men = (2 × 8) boys = 16 boys

If 20 boys can make 20 cricket bats in 10 days,
8 men and 4 boys or, (16 + 4) = 20 boys can make in 20 days = (20 × 2) cricket bats
= 40 cricket bats

Question: M and N can do a piece of work in 20 days and 12 days respectively. M started the work alone and then after 4 days, N joined him till the completion of the work. How long did the work last?

Solution:
work done by m in 4 days = (1/20) × 4 = 1/5
∴ Remaining work = 1 - (1/5) = 4/5

(M + N)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now, 2/15 work is done by M and N in 1 day.
So, 4/5 work will be done by M and N in = (15/2) × (4/5)
= 6 days

∴ Total time taken = (6 + 4) days = 10 days

Question: A military camp had enough food supplies to last for a certain number of days. After 10 days, 1/5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

Solution:
Let, initially there be 'x' men having foods for y days
After 1/5 of the men left = x - (x/5)
= 4x/5

After 10 days,
x men had foods for (y - 10) days
∴ 1 man had foods for x(y - 10) days
∴ 4x/5 men had foods for = {5x(y - 10)}/4x days
= 5(y - 10)/4 days

ATQ,
5(y - 10)/4 = y
⇒ 5y - 50 = 4y
∴ y = 50

Question: 3 men, 4 women, and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

Solution:
Let 1 woman's 1 day work = x.
Then, 1 man's 1 day work = x/2 and 1 child's 1 day work  x/4.

ATQ,
(3x/2) + 4x + (6x/4) = 1/7
⇒ 28x/4 = 1/7
∴ x = 1/49

1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7.

Question: 64 persons can dig a trench 50m long, 2m wide, and 2m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75m long, 4m wide, and 3m deep?

Solution:
The volume of 50m long, 2m wide, and 2m deep is (50 × 2 × 2) m³ = 200 m³
The volume of 75m long, 4m wide, and 3m deep is (75 × 4 × 3) m³ = 900 m³

64 persons by working 12 hours daily can dig 200m³ in = 5 days.
∴ 1 person by working 1 hour daily can dig 1 m³ in = (5 × 64 × 12)/200 days.
∴ 80 persons by working 8 hour daily can dig 900 m³ in = (5 × 64 × 12 × 900)/(200 × 80 × 8) days.
= 27 days

Question: P can complete work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together, working 8 hours a day, in how many days can they complete the work?

Solution:
P can complete the work in (12 × 8) hrs = 96 hrs 
Q can complete the work in (8 × 10) hrs = 80 hrs 
Therefore, P's 1 hour work = 1/96 and Q's 1 hour work = 1/80

(P + Q)'s 1 hour's work = (1/96) + (1/80)
= 11/480

So both P and Q will finish the work in 480/11 hrs  
Therefore, Number of days of 8 hours each = (480/11) × (1/8) = 60/11

Question: A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together?

Solution:
3 men's 1 days work = 1/20 and 5 boy's 1 day's work = 1/30
(3 men + 5 boy)'s 1 day's work = (1/20 + 1/30)
= 5/60 = 1/12

∴ 3 men and 5 boys will complete the work in 12 days.

Question: Jahir is twice as good as a workman as Kabir. When they work together they can finish a task in 16 days. If Kabir works alone, in how many days he will complete the task?

Solution:
(Jahir + Kabir)'s one-day work = 1/16
As per the question, Jahir can finish twice as much work as finished by Kabir in a given duration of time.

Therefore, 2/3 of their one-day work will be completed by Jahir and 1/3 of their one day work will be completed by Kabir.

So, Kabir's one day work will be = (1/16) × (1/3) = 1/48
So, Kabir's will take 48 days to complete the task.

Question: A cistern can be filled by two pipes P & Q in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?

Solution: 
In 1 min both pipes can fill = (1/20) + (1/30)
= (3 + 2)/60
= 5/60 = 1/12
In 10 min second pipe can fill = (1/30) × 10 = 1/3 part

Part of cistern filled by both the pipes = 1 - 1/3
= (3 - 1)/3 = 2/3

1/12 part is filled in 1 min
∴ 2/3 part will be filled in (12 × 2)/3 = 8 min
Hence, the first pipe should be turned off after 8 min.