Question

There are two inlet pipes A and B connected to a tank. A and B can fill the tank in 32 h and 28 h, respectively. If both the pipes are opened alternately for 1 h, starting with A, then in how much time (in hours, to nearest integer) will the tank be filled?

• A. 22
• B. 30
• C. 36
• D. 24

Answer 1

Answer:

B. 30

Solution:

Given:

Pipe A and B can fill the tank in 32 h and 28 h

Concept used:

Total work = Efficiency of the pipes × time taken by the pipes

Calculation:

Let the total work be 224 units (LCM of 32, 28)

The efficiency of pipe A = 224/32 = 7 units/h

The efficiency of pipe B = 224/28 = 8 units/h

Now,

In 1st hour A completes 7 units

In the next 1 hour, B completes 8 units

So, in 2 hours 15 units are filled in the tank

In 28 hours, 15 × 14 = 210 units will be filled in the tank

The remaining 14 units,

 Now A will work on 29^th hour,

210 + 7 = 217 units, 

Now B will work and will complete the work, 

$29\frac{7}{8}$

The required answer is 30.