Bank Math Master

Question: Tamim can do a work in 12 days and Sakib in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is:

Solution:
Tamim's 1 day's work = 1/12
Sakib's 1 day's work = 1/15

∴ (Tamim + Sakib)'s 1 day's work = (1/12 + 1/15) part
= (5 + 4)/60 part
= 9/60 part
= 3/20 part

∴ (Tamim + Sakib)'s 5 day's work = [5 × (3/20)] part
= 15/20 part
= 3/4 part

Therefore, Remaining work = (1 - 3/4) part
= 1/4 part

Question: A man completes 1/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?

Solution:
Work done = 1/8
Balance work = 1 - (1/8) = 7/8

A man completes 1/8 of a job in 10 days
A man completes 1 part of a job in 10 × 8 days
= 80 days

∴ More days required = 80 - 10 
= 70 days.

Question: How long will it take for two pipes to fill a tank together when they can fill it alone in 10 hours and 15 hours, respectively?

Solution:
together in one hour they can fill = 1/10 + 1/15
= 5/30
= 1/6

so, the total time to fill the tank is = 6 hours

Question: A, B and C can do a piece of work in 24, 36 and 72 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? 

Solution:
A's 2 day's work = (1/24) × 2 = 1/12
∴ (A + B + C)'s 1 day's work = 1/24 + 1/36 + 1/72

= 1/24 + 1/36 + 1/72
= (3 +2 +1)/72
= 6/72
= 1/12

Work done in 3 days = 1/12+ 1/12
= 2/12
= 1/6

Now,
1/6 work is done in 3 days.
∴ Whole work will be done in (3 × 6) = 18 days

Question: 12 women can complete a piece of work in 10 days. 10 men can complete the same work in 8 days. What is the ratio of the work capacity of one man to one woman?

Solution:
12 women can complete a piece of work in 10 days.
∴ 1 woman can complete a piece of work in 10 × 12 = 120 days.

∴ 1 Woman's 1 day's work = 1/(12 × 10) 
= 1/120
∴ One woman's 1 day's work = 1/120

Similarly, 
Men's 1 day's work = 1/(10 × 8) = 1/80
∴ One man's 1 day's work = 1/80

∴ Ratio of capacity of one man to one woman = (1/80) : (1/120)
= 120 : 80
= 3 : 2

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 8 hours. Another pipe alone can fill two tanks in - 

Solution: 
Let, the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/8 + 1/X
= (X + 8)/8X

ATQ,
⇒ 8X/(X + 8) = 6
⇒ 8X = 6 × (X + 8) hours.
⇒ 2X = 48
⇒ X = 24

∴ to fill two tanks it will take = 48 hours

Question: Rina completes 60% or 3/5 of a work in 12 days. Then she calls in Sima, and together they finish the remaining work in 6 days. How long would Sima alone take to complete the whole work?

Solution:
Here,
Rina does 3/5 of the work in 12 days
in one day, she does = (3/5 ÷ 12)
= 3/60
= 1/20 part

In 6 days, she does 6/20 = 3/10 part
work remaining = 2/5

Together, they do 2/5 in 6 days
Together in one day = (2/5) ÷ 6
= 2/30
= 1/15

Rina one day = 1/20
Sima one day = 1/15 - 1/20
= (4-3)/60
= 1/60

∴ Sima alone will take 60 days to complete the whole work.

Question: An outgoing pipe is attached to a tank that can empty it in 18 hours. An ingoing pipe is connected to the tank that can fill it in 9 hours. How much time will it take to fill the half-full tank?

Solution: 
ingoing pipe in one hour can fill = 1/9
outgoing pipe in one hour can empty = 1/18

in one hour, the total fill up = 1/9 - 1/18 = 1/18

∴ To fill the tank it will take = 18 hours.
∴ To fill half the tank it will take = 18/2
= 9 hours

Question: A pipe can fill 1/4th of a tank in 30 minutes. How much time will it take to fill two tanks?

Solution:
A pipe can fill 1/4th of a tank in 30 minutes
∴ A pipe can fill 1 part or full of a tank in = (4 × 30)
= 120 minutes = 2 hours

One tank is filled in 2 hours
∴ two tanks is filled in = 4 hours

Question: If 12 men or 18 boys can make 360 baskets in 15 days, then how many baskets will be made by 10 men and 15 boys in 15 days?

Solution:
Here,
12 men = 18 boys
∴ 1 man = 18/12 boys
= 3/2 boys

∴ 10 men = (3/2) × 10 = 15 boys
∴ 10 men and 15 boys = 15 boys + 15 boys
= 30 boys

18 boys can make 360 baskets in 15 days
∴ 1 boy can make in 15 days = 360/18 = 20 baskets
∴ 30 boys can make in 15 days = 20 × 30 = 600 baskets

∴ 10 men and 15 boys can make 600 baskets.

Question: Pipe A fills a tank in 40 seconds, pipe B in 60 seconds, and pipe C empties it in 30 seconds. Initially, A and B are opened, and after 8 seconds, C is also opened. In how much more time will the tank be completely filled?

Solution:
Let the capacity of the tank be LCM of 40, 60, 30 = 120 units.

Efficiency of A = 120/40 = 3 units/second
Efficiency of B = 120/60 = 2 units/second
Efficiency of C = –120/30 = –4 units/second

(A + B open) for first 8 seconds,
Combined efficiency = 3 + 2 = 5 units/second
Work done in 8 seconds = 8 × 5 = 40 units
Remaining work = 120 – 40 = 80 units

Now when all three pipes open,
Combined efficiency = 3 + 2 – 4 = 1 unit/second
More time required = 80 ÷ 1 = 80 seconds

Question: A petrol tank is initially one-third full. After removing 5 gallons of petrol, the tank becomes one-fifth full. What is the total capacity of the tank in gallons?

Solution:
Let,
The capacity of the tank in gallons is x gallons.

According to question,
⇒ (x/3) - 5 = x/5
⇒ (x - 15)/3 = x/5
⇒ 5(x - 15) = 3x
⇒ 5x - 75 = 3x
⇒ 5x - 3x = 75
⇒  2x = 75
∴ x = 37.5 gallons

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 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. So C works for y days
Therefore, A works for (y - 8) days B works for (y - 12) days.

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

Question: 2/5 part of the tank is full of water. When 24 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution: 
Let the total capacity of the tank be 5x liters.
Then, water in the tank = 2/5 × 5x = 2x liters.

When 24 liters of water is taken out, the tank becomes empty.
It means the water taken out = water present in the tank.
∴ 2x = 24 litres
⇒ x = 12 litres

∴ Capacity of the tank = 5x
= 5 × 12
= 60 liters.

Question: If the workforce is tripled, how much longer will it take to finish the task?
​
Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর তিনগুণ = ৩x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
∴ ৩x জন কাজটি করে = xn/৩x
= n/৩ সময়ে বা ১/৩ সময়ে।

Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 24 minutes, then the slower pipe alone will be able to fill the tank in-

Solution:
Let,
the slower pipe alone fill the tank in x minutes.
Then, Faster pipe alone will fill it in x/4 minutes.

ATQ,
(1/x) + (4/x) = 1/24
⇒ 5/x = 1/24
∴ x = 120

∴ The slower pipe alone fill the tank in 120 minutes
= (120/60) hours
= 2 hours