water filling

/A+1/B=5/6---(1)

1/A+1/C=2/3---(2)

1/B+1/C=1/2---(3)

(2)-(3)=1/A-1/B=1/6---(4)

(4)+(1)=2/A=1

A=2

Now substitute A into equations 1, 2, 3, or 4 to get B and C.

B=3

C=6

1/A+1/B+1/C=1/X

X= The number of hours it takes pumps A, B, and C, operating simultaneously to fill the tank

1/2+1/3+1/6=1/X

1=1/X

X=1 hour.

Its a very simple question.
We have 3 equations from Work-time theory.

1/a + 1/b = 5/6

1/b + 1/c = 1/2

1/c +1/a = 2/3

add all the 3

2*(1/a + 1/b + 1/c) = 2

(1/a + 1/b + 1/c) = 1

so,answer 1 hr.

A point of advice, please revise some basic Quant concepts, so that you don't get caught up with these simple questions.

Hope this helps

gmat740, why do you multiply by 2 the addition?

1/a + 1/b + 1/a + 1/c + 1/b + 1/c = 2 * (1/a + 1/b + 1/c)

shibal wrote:gmat740, why do you multiply by 2 the addition?

When you add all the 3 three equations wriiten below:

1/a + 1/b = 5/6

1/b + 1/c = 1/2

1/c +1/a = 2/3

LHS = (1/a +1/b) +( 1/b + 1/c) +(1/c +1/a )

We can see that we have 2(1/a) , 2(1/b) and 2(1/c)

thus it can be simplified as 2*(1/a +1/b +1/c)

Hope this Helps

thanks,i got it, but why do you do the following?

2*(1/a + 1/b + 1/c) = 2

why equal to 2?

shibal,

Think of the equations this way:

a + b = 5/6

a + c = 2/3

b + c = 1/2

where, a, b, and c represent the work rates of a, b, and c.

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

2a + 2b + 2c = 5/6 + 4/6 + 3/6

2a + 2b + 2c = 12/6

2a + 2b + 2c = 2

This above equation tells us that it takes 2 of each of the workers 1/2 hour to complete the job. But, we only need one of each worker. Therefore factor the 2.

2(a + b + c) = 2

a + b + c = 1

Therefore, a, b, and c working together complete the job in 1 hour.