Bank Math Master

Question: Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the field?

Solution: 
সুমিত একদিনে করে ১/৬ অংশ কাজ 

আমিত একদিনে করে (১/৪) - (১/৬) 
= ১/১২ অংশ কাজ 

সম্পূর্ণ কাজটি করতে অমিতের সময় লাগবে = ১২ দিন 

Question: A cistern can be filled by two pipes 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 min 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, first pipe should be turned off after 8 min.

Question: A man and a boy received Tk. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?

Solution: 
Man's wage = 3 boy's wage
Daily wages for them = 800/5
 = 160

A man and a boy = 4 boys 
4 boys' wage  = 160
4 boys' wag = 160
⇒ boy's wage = Tk. 40

প্রশ্ন: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

সমাধান: 
Suppose,
pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

Now,
1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
∴ x = 35

∴ pipe A alone takes 35 hours to fill the tank.

Problem: If three workers can mow a lawn in 4 hours, how many workers are needed to mow the lawn in 2 hours?

Solution: 
৪ ঘণ্টায় শেষ করতে লোক লাগে ৩ জন 
২ ঘণ্টায় শেষ করতে লোক লাগে (৪ × ৩/২) জন 
= ৬ জন 

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution: 
3 pumps need 2 × 8 hours = 16 hours
1 pump needs  16 × 3  hours
4 pumps need (16 × 3)/4 hours
= 12 hours

Question: By working 5 hours a day, A can complete work in 8 days, and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in -

Solution:
Working 5 hours a day,
A can complete the work in 8 days.
A can complete the work in = 5 × 8 = 40 hours.

Working 6 hours a day, B can complete the work in 10 days.
B can complete the work in = 6 × 10 = 60 hours.
(A + B)'s 1 hour's work,
= 1/40 + 1/60
= (3 + 2)/120
= 5/120
= 1/24

Hence, A and B can complete the work in 24 hours.
Working 8 hours a day
They require = 24/8 = 3 days to complete the work.

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days  

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days.

Question: Pipe A fills a tank in 20 minutes. Pipe B can fill the same tank 5 times as fast as Pipe A. If both the pipes are kept open when the tank is empty, when will the tank be full?

Solution: 
নল A ২০ মিনিটে পূর্ণ করে।
নল B পূর্ণ করে = ২০/৫ মিনিটে 
= ৪ মিনিটে 

দুটি নল একসাথে ১ মিনিটে পূর্ণ করে = (১/২০) + (১/৪) মিনিটে 
= (১ + ৫)/২০
= ৬/২০ মিনিট 

দুটি নল ৬/২০ অংশ পূর্ণ করে = ১ মিনিটে
 দুটি নল ১ অংশ পূর্ণ করে = ২০/৬ মিনিটে
= (২০ × ৬০)/৬
= ২০০ সেকেন্ড

Question: An outlet pipe can empty a cistern in 3 hours. In what time will it empty 2/3 part of the cistern? 

Solution: 
সম্পূর্ণ অংশ খালি করতে সময় লাগে ৩ ঘণ্টা 
২/৩ অংশ খালি করতে সময় লাগে ৩ × ২/৩ ঘণ্টা 
= ২ ঘণ্টা 

  প্রশ্ন: Zisan completed the school project in 20 days. How many days will Ali take to complete the same work if he is 25% more efficient than Zisan?

সমাধান:
আলী জিসানের চেয়ে ২৫% দক্ষ।

অর্থাৎ,
জিসান ১২৫ দিন সময় নিলে আলী নিবে ১০০ দিন 
∴ জিসান ১ দিন সময় নিলে আলী নিবে ১০০/১২৫ দিন
∴ জিসান ২০ দিন সময় নিলে আলী নিবে (১০০ × ২০)/১২৫ দিন
= ১৬ দিন 

Question: A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time taken by one tap to fill half the tank = 4 hrs
Remaining part after 4 hrs = (1 - 1/2) = 1/2
Part filled by the four taps in 1 hours = 4 × (1/8) = 1/2

Total time = 4 + 1 = 5 hrs

Question: 3/4 part of the tank is full of water. When 18 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution: 
3/4 part of the tank is 18 liters

Capacity of the tank is = 18 × 4/3 
= 24 liters

Question: A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is =?

Solution: 
Let the time taken by B and C = x days
∴ Time taken by A = 3x days
∴ Part of the work done by A, B and C in 1 day = 1/x + 1/3x = (3 + 1)/3x = 4/3x

∴ 4/3x = 1/24
⇒ 3x = 4 × 24
⇒ x = 96/3
∴ x = 32 days

∴ Time taken by A = 32 × 3 = 96 days.

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

Solution: 
একটি পাইপ চৌবাচ্চা পূর্ণ করতে পারে ২ ঘণ্টায় বা ১২০ মিনিটে  
১ মিনিটে পূর্ণ করে ১/১২০ অংশ 

একটি ছিদ্র থাকায় তা পূর্ণ করতে পারে ১৪০ মিনিটে 
১ মিনিটে পূর্ণ হয় ১/১৪০ মিনিটে 

ছিদ্র দিয়ে ১ মিনিটে খালি হয় = (১/১২০) - (১/১৪০)
= (৭ - ৬)/৮৪০
= ১/৮৪০ অংশ 

সম্পূর্ণ অংশ খালি করতে সময় লাগে = ১/১/৮৪০ মিনিট 
= ৮৪০ মিনিটে 
= ৮৪০/৬০ ঘণ্টায় 
= ১৪ ঘণ্টায়