ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If Rafi and Suman together can complete a job in 12 days. If Rafi alone can finish the job in 20 days, in how many days can Suman alone complete the work?

Solution: 
Rafi and Suman together can complete a piece of work in 12 days
Rafi and Suman together can complete in 1 day = 1/12 

Rafi alone in 20 days
Rafi alone in one day = 1/20

∴ Suman complete in one day = (1/12) - (1/20)
= (5 - 3)/60
= 2/60
= 1/30

∴ Suman can complete the work in 30 days

Question: If 10 men or 18 women can do a work in 50 days then how many days would it take 25 men and 15 women to do twice the work?

Solution:
Here,
10 men = 18 women
∴ 1 men = 18/10 women
∴ 25 men = (18 × 25)/10 women
= 45 women

∴ 25 men and 15 women = (45 + 15) = 60 women

ATQ,
18 women can do the work in 50 days
∴ 1 women can do the work in = (50 × 18) days
∴ 60 women can do the work in (50 × 18)/60 days
= 15 days

Hence to do twice the work time need = (15 × 2) = 30 days

Question: Musa can do 1/4 of a work in 6 days. In how many days will he complete the work?

Solution:
Musa can do 1/4 of a work in 6 days.
∴ He will complete the work in = 6 × 4 = 24 days 

∴ Musa will complete the work in 24 days.

Question: 30 workers can build 60 machines working 4 hours per day. How many extra workers are required to produce 90 machines working 6 hours per day?

Solution:
4 hours to build 60 machines by 30 workers
1 hour to build 1 machine by = (30 × 4)/60 workers
6 hours to build 90 machines by = (2 × 90)/6 workers
= 30 workers

∴ extra workers = (30 - 30) = 0 workers

Question: P can complete a piece of work in 18 days, while Q can complete the same work in 36 days. If both P and Q work together, in how many days will they be able to complete the entire work?

Solution:
Given that,
P can do a piece of the work in 18 days and Q can do same work in 36 days

Now,
Let the total work = LCM(18, 36) = 36

Hence, total work = 36 units

Thus,
P does each day = 36 ÷ 18 = 2 units
Q does each day = 36 ÷ 36 = 1 unit

Hence, time taken by them to finish the work together = 36 ÷ (1 + 2) = 12 days.

∴ In 12 days working together they will complete the entire work.

Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles

∴ Required number of motorcycles = 40 - 24 = 16

So the ferry can carry 16 more motorcycles along with the 15 trucks.

Question: A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left-

Solution:
Man's 1 day's work = 1/20
Woman's 1 day's work = 1/15

∴ (Man + woman)'s 1 day's work = (1/20) + (1/15)  = (3 + 4)/60 = 7/60
∴ (Man + woman)'s 5 day's work = (7/60) × 5 = 7/12

Thus, Remaining work = 1 - (7/12) = (12 - 7)/12 = 5/12

∴ The fraction of the work that is left = 5/12

Question: John can paint 60 walls in 20 minutes. Emma can paint 9 walls in 15 minutes. Working together, how many walls can they paint in 25 minutes?

Solution:
John can paint in 1 min = 60/20 = 3 walls
Emma can paint in 1 min = 9/15 = 3/5 walls

∴ Working together they can paint in 1 min = (3 + 3/5) = 18/5 walls

∴ They can paint in 25 min = (18 × 25)/5 = 90 walls

So John and Emma can paint 90 walls together in 25 minutes.

Question: Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 5400. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

Solution:
Anik's 1day work = 1/6
Bishal's 1 day work = 1/8

∴ (Anik + Bishal + Dinesh)'s 1 day work = 1/3

∴ Dinesh's 1 day work = (1/3) - (1/6) - (1/8) = (8 - 4 - 3)/24 = 1/24

So, Dinesh's 3 day work = 3 × (1/24) = 1/8
If Dinesh contributed 8th part of work then he will receive 8th part of total payment

∴ Dinesh should be paid = 5400 × (1/8) = Tk. 675

Question: If 4 workers can assemble a car in 6 hours, how long would it take 15 workers to assemble the same car?

Solution:
Given,
4 workers can assemble a car in 6 hours
∴ 1 workers can assemble a car in (6 × 4) hours
∴ 15 workers can assemble a car in (24/15) hours
= (24 × 60)/15 minutes
= 96 minutes

Question: In a factory, 20 people can make 20 toys in 15 days working 10 hours per day. Then, in how many days can 25 persons make 30 toys working 20 hours per day?

Solution:
Here,
M₁ = 20, M₂ = 25
D₁ = 15, D₂ = ? 
T₁ = 10, T₂ = 20,
W₁ = 20 and W₂ = 30.

We know,
M₁ × D₁ × T₁ × W₂ = M₂ × D₂ × T₂ × W₁
⇒ 20 × 15 × 10 × 30 = 25 × D₂ × 20 × 20
∴ D₂ = 9

Thus, the required day = 9 days

Question: P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

Solution:
Given that,
(P + Q)'s 1 day's work = 1/3 
(Q + R )'s 1 day's work= 1/4
and
(R + P)'s 1 day's work = 1/12

Now, (P + Q) + (Q + R) + (R + P) = 2(P + Q + R)'s 1 day's work = (1/3) + (1/4) + (1/12)
= (4 + 3 + 1)/12
= 8/12 = 2/3
∴ (P + Q + R)'s 1 day's work = 2/(3 × 2) = 1/3

So, P + Q + R can complete the job in = 3 days

Question: P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?

Solution:
P's 1 day's work = 1/(x + 3) part
Q's 1 day's work = 1/(x + 12) part
and (P + Q)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x
⇒ (2x + 15)/(x² + 15x + 36) = 1/x
⇒ 2x² + 15x = x² + 15x + 36
⇒ 2x² + 15x - x² - 15x = 36
⇒ x² = 36
∴ x = 6

Question: A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?

Solution: 
Let the work be completed in y days. C works for y days
Therefore, A works for (y - 8) days
B works for (y - 12) days.

According to the question,
{(y-8)/36} + {(y - 12)/54} + (y/72) = 1
⇒ 6(y - 8) + 4 (y - 12) + 3y = 216
⇒ 6y - 48 + 4y -  48 + 3y = 216
⇒ 13y = 216 + 96 = 312
⇒ y = 312/13
∴ y = 24