ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: Akib can do 1/6 of a work in 7 days. In how many days will he complete the work?

Solution:
Akib can do 1/6 of a work in 7 days
∴ he will complete the work in (6 × 7) days
= 42 days

∴ Akib will complete the work in 42 days.

Question: Three workers can do a job in 12 days. Two of the workers work thrice as fast as the third. How long would it take one of the faster workers to do the job himself?

Solution:
Let,
The first and second worker need P days.
Third worker needs 3P days.

ATQ,
(1/P) + (1/P) + (1/3P) = 1/12
⇒ (3 + 3 + 1)/3P = 1/12
⇒ 7/3P = 1/12
⇒ 3P = 84
⇒ P = 84/3
∴ P = 28

So the one faster worker alone will take 28 days to complete the job.

Question: Ruma can paint 70 walls in 14 minutes. Salma can paint 45 walls in 9 minutes. Working together, how many walls can they paint in 35 minutes?

Solution:
Ruma can paint in 1 minute = 70/14 = 5 walls
Salma can paint in 1 minute = 45/9 = 5 walls

∴ Working together they can paint in 1 minute = (5 + 5) = 10 walls

∴ they can paint in 35 minutes = (35 × 10) = 350 walls

Question: In a camp of soldiers there was a stock of food for 90 days for 6000 soldiers. After 30 days, 2400 soldiers left the barracks. For how many days shall the leftover food last for the remaining soldiers?
Let,
the remaining food last for P days
6000 soldiers had provision for 90 days
3600 soldiers had provision for P days

ATQ,
3600/6000 = 60/P
⇒ 3/5 = 60/P
⇒ 3P = 300
⇒ P = 300/3
∴ P = 100

The remaining food last for 100 days for the remaining soldiers.

Question: A and B can complete a piece of work in 18 days and 12 days respectively. They got a contract to complete the work for TK. 60000. The share of A in the contracted money will be-

Solution:
Ratio of number of days taken by A and B to complete the work = 18 : 12 = 3 : 2
∴ Ratio of efficiency of A and B = 2 : 3

Let their shares is in the ratio of 2x and 3x
Now,
2x + 3x = 60000
or, 5x = 60000
∴ x = 60000/5 = 12000

∴ share of A = 2x = 2 × 12000 = 24000 Taka

Question: Working alone, Rasel can complete a certain kind of job in 8 hours. Rasel and Shima working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can Shima working alone, complete one of these jobs?

Solution:
Working together Rasel and Shima can complete the job in 6 hours
which means
(1/Rasel) + (1/Shima) = (1/6)
⇒ (1/8) + (1/Shima) = (1/6)      [Rasel can complete the job in 8 hours]
⇒ (1/Shima) = (1/6) - (1/8)
⇒ (1/Shima) = (4 - 3)/24
∴ (1/Shima) = 1/24

so, Shima working alone can complete the job in 24 hours

Question: If a half kg of tomato costs 80 taka, how many taka will 300 gm cost?

Solution:
Let the required cost be P TK
Less weight : Less cost (Direct proportion)
500 : 300 : : 80 : P
⇒ 500/300 = 80/P
⇒5/3 = 80/P
⇒ P = (3 × 80)/5
∴ P = 48

Question: A group of women decided to do a job in 5 days. But since 15 women dropped out every day, the job completed at the end of the 8th day. How many women were there at the beginning?

Solution:
Let X be the initial number of women then,
According to the question,
5X = X + (X - 15) + (X - 30) + (X - 45) + (X - 60) + (X - 75) + (X - 90) + (X - 105)
⇒ 5X = 8X - 420
⇒ 8X - 5X = 420
⇒ 3X = 420
⇒ X = 420/3
∴ X = 140 women

Question: A group of 8 men can paint a house in 20 days. If they want to complete the painting in 16 days, how many more men should they add to the group?

Solution:
২০ দিনে কাজ শেষ করতে পারে ৮ জন
১ দিনে কাজ শেষ করতে পারে (২০ × ৮) জন
১৬ দিনে কাজ শেষ করতে পারে (২০ × ৮)/১৬ জন
= ১০ জন

∴ অতিরিক্ত (১০ - ৮) বা ২ জন যোগ করতে হবে।

Question: There is a group of 7 boys and 4 girls. The two groups working together can do five times as much work as a boy and a girl. Ratio of working capacities of a boy and a girl is:

Solution:
Let 1 boy's 1 day's work = x
And 1 girl's 1 day's work = y
Now,
(7 boys + 4 girls)'s work = 7x + 4y
Given,
7x + 4y is equal to 5 times work done by a boy and a girl
Thus,
7x + 4y = 5(x + y)
⇒ 7x + 4y = 5x + 5y
⇒ 7x - 5x = 5y - 4y
⇒ 2x = y
⇒ x/y = 1/2
⇒ x : y = 1 : 2

Hence, the required ratio is 1 : 2

Question: Rakib can do a piece of work in 15 days, Rakib and Asif together can do in 12 days. If Asif does the work only for half a day daily then in how many days the work will be completed ?

Solution: 

Rakib's 1 day work = 1/15

Since, Rakib and Asif can together complete in 12 days
i.e. (Rakib + Asif)'s 1 day work = 1/12

Then,
Asif's 1 day work,
= (1/12) - (1/15) = (5 - 4)/60 = 1/60

If Asif Works only for half a day daily, then his 1 day work becomes (1/2) × (1/60)
  = (1/120)

Therefore, 1 day work of both Rakib and Asif,
=(1/15) + (1/120) = ( 8 + 1)/120 = 9/120

Hence, the work will be completed in 120/9 = 40/3 days

Question: A man completes (1/3) of a job in 13 days. At this rate, how many more days will it take him to finish the job?

Solution:
 

Work done = 1/3

Balance work =(1−1/3) = 2/3

Less work, Less days ( Direct proportion)
Let the required number of days be x
Then,
⇔ (1/3) : (2/3) : : 13 : X
⇔ (1/3)/(2/3) = 13/X
⇔ 1/2 = 13/X
⇔ X = 13 × 2 = 26 days

Question: 48 men can complete a piece of work in 18 days. In how many days can 36 men complete the same piece of work?

Solution:
Let the required number of days be x
Less men, More days (Indirect proportion)
∴ 36 : 48 : : 18 : x
⇔ 36/48 = 18/x
⇔ 36x = 18 × 48
⇔ x = (18 × 48)/36
∴ x = 24

Question: A is twice as good a workman as B and therefore can finish a job 30 days earlier than B. Working together, in how many days can they finish the job?

Solution:

Given,
A is twice as good workman as B. Means,
A = 2B
Let B can finish work in X days, then A will finish same work in (X - 30) days alone
Now,
BX = 2B × (X - 30)
⇒ BX = 2BX - 60B
∴ X = 60 days
B can finish work in 60 days, then A can finish the work in 30 days.
One day work of B = 1/60

One day work of A = 1/30

One day work of (A+B) = (1/60) + (1/30) ⇒ (1+2)/60 ⇒ 3/60 ⇒ 1/20

So, they can finish work together in 20 days.