Mathematics on unitary methods

A  can  complete a  work in 45 days  while B can complete the work in  50 days and  C  can  do in 55 days.

After  8 days of working  by A , B joins with A and on  20 day C joined for till completion of rest of the work.

How much time it took for the total work ?

SOLUTION

Let the total work  is  1

A  can complete  the  work  in 45 days  when does alone.

So in 1 day A can do  1/45  parts of the work.

A  worked till 8 days. So in  8 days  8/45 parts of the work is completed=

0.17778

parts

Now  B can complete the work in 50 days

So in 1 day B can do 1/50 parts of the work.

A and B did work upto 20 th. day.

In one day A and B  in together does  (1/45+ 1/50 ) parts of the work = 19/450 parts

For 12 days total work done is =12* 19/450   =

0.50667

Total work completed = 0.17778+0.50667=

0.68445

Work left  = 1 - 0.68445 =

0.31555

parts

Now, this 0.31555 parts of the work A, B and C worked together

C can do  1/55 parts of the work in one day.

In one day   1/45 +1/55+ 1/60 =

0.057071

parts of the work can be executed

Work left is  0.31555 , so time will be

5.529078

days

Total time taken  A alone 8  days

And A and B  12 days

A,B and C  together 5.53 days

25.53

days.

ANS

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when both are filling simultaneosly

solution :

Let   we consider the filled up tank quantity is 1

In 10 hours the tank is filled up by one line

so , in 1 hour the tank is filled up by 1/10  parts quantity

By other line in 14 hrs. the tank can be filled

so in 1 hour the tank is filled up by 1/14 parts

Now , when both the filling lines are being used ,

simultaneously  1/10 + 1/14 parts are being filled up in 1 hour

0.1714

parts are filled up in 1 hour when both the filling lines are opened.

Now let us calculate

0.1714 parts are filled up in 1 hour

1 that is full tank is filled up 1/0.1714 hr=

5.8343

hrs.

the tank will be filled up in 5.8384 hrs.

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when  first filling line is opened for 5 hrs . And second line started

to fill the tank. calculate the time taken for filling the tank

solution

First filling line was opened for 5 hours.

Let us suppose that the filling volume of the tank is 1

first filling line takes 10 hrs. to completely fill up the tank

so in 1 hr 1/10 parts of the tank is filled up

In five hours 5*1/10 parts

0.5

parts of the tank is filled up

remaining part of the tank will be  1-0.5 = 0.5 parts

now let us take the second line  which takes 14 hrs to fill up the full tank

but in this case 0.5 parts that is half of the tank  needs to be filled up

so , in mathematically to deduce

1 volume of  tank is filled up in 14 hours

0.5 volume of tank will require 14 * 0.5 = 7 Hrs.

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when  second filling line is opened for 5 hrs . And first line started

to fill the tank. calculate the time taken for filling the tank

solution

let us consider the volume, that is filled up tank is  1 unit

the second filling line takes 14 hrs to fill up the tank

so in one hour second filling line fills up 1/14 volume of the tank

Second filling line opened for five hours

total filled up volume by the second line till five hours is  5/14 unit

0.3571

unit

we have taken

total volume as 1

so empty tank is 1- 0.3571

0.6429

unit

now the  first line is started which fills up the tank in  10 hrs. so in one hour

tank filled up by 1/10 unit

now we can say that  1/10 unit is filled up in  1 hour

1 unit will be filled up in  10  hours

0.6429 unit will be filled  10*0.6429

6.429

hrs.