Pipe X can empty a completely filled tank in 60 hours. Pipe Y and X together can fill an empty tank completely in (z+6) hours. The efficiency of pipe Y is 40% more than the efficiency of pipe U. Pipe Y and U together can fill the empty tank together in 30 hours. Find the value of ‘z’

The correct option is 354.

Let us solve this problem step-by-step to find the value of z.

Step 1: Determine the individual efficiencies of Pipe Y and Pipe U

Let the efficiency (work done per hour) of Pipe U be denoted by U.

It is given that the efficiency of Pipe Y is 40% more than the efficiency of Pipe U.

Therefore, the efficiency of Pipe Y can be written as:

$Y=U+0.40U=1.4U=\frac{7}{5}U$

It is also given that Pipe Y and Pipe U together can fill the empty tank completely in 30 hours.

Thus, their combined rate of work per hour is:

$Y+U=\frac{1}{30}$

Substituting $Y=\frac{7}{5}U$ into the combined rate equation:

$\frac{7}{5}U+U=\frac{1}{30}$

$\frac{12}{5}U=\frac{1}{30}$

$U=\frac{1}{30}\times \frac{5}{12}=\frac{1}{72}$

Now, calculate the rate of Pipe Y:

$Y=\frac{7}{5}\times \frac{1}{72}=\frac{7}{360}$

Step 2: Find the combined rate of Pipe Y and Pipe X

Pipe Y fills the tank, while Pipe X empties the tank.

The emptying rate of Pipe X is given as:

$X=\frac{1}{60}$

When Pipe Y and Pipe X work together, the net rate of filling the tank per hour is:

$\text{Net Rate}=Y-X=\frac{7}{360}-\frac{1}{60}$

Taking the common denominator (360):

$\text{Net Rate}=\frac{7-6}{360}=\frac{1}{360}$

Step 3: Calculate the total time and solve for z

Since the net rate is 1/360 tank per hour, Pipe Y and Pipe X together take 360 hours to fill the tank completely.

The problem states that they fill the tank completely in (z + 6) hours.

Equating the two expressions for time:

$z+6=360$

$z=360-6$

$z=354$

Thus, the value of z is 354.