Pumps A,B and C operate

[JA]

Hi,

Could someone please help me with this question, I got it wrong in my GMAT Prep.

Thanks
JA

[blue_lotus]

In work problems the total part of work to be completed is always 1

Let A take 'a' hours to fill the tank alone .
-Means it takes 'a' hours to complete the total part (1).
-This also means A does 1/a part of the work per hour.

Let B take b hours to fill the tank alone
Let C take c hours to fill the tank alone


A and B can fill the tank in 6/5 hours to fill the tank
Therefore in one hour they can fill 5/6 part of the tank or say 5/6 part of the work
1/a + 1/b = 5/6 ---------(1)


A and C can fill the tank in 3/2 hours to fill the tank
Therefore in one hour they can fill 2/3 of the tank .
1/a + 1/c = 2/3 ---------(2)


B and C can fill the tank in 2 hours to fill the tank
Therefore in one hour they can fill 1/2 of the tank .
1/b + 1/c = 1/2 ---------(3)


Adding equations 1 ,2 and 3 we get

2[1/a + 1/b + 1/c] = 5/6 + 2/3 + 1/2 = 2

[1/a + 1/b + 1/c] = 1

This means in one hour A , B and C can complete 1 part of the job
Therefore the total time taken by all the three of them = 1 /( work done by 2 in one hour) = 1/1 =1

[JA]

Great explanation.

Thanks blue_lotus!!!