Question

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

• A. 140
• B. 120
• C. 144
• D. 264

Answer 1

Answer: (C)

144

Answer 2

Let's rephrase the given information and calculations:

We designate the filling rate of pipe A as 'a' and the emptying rate of tank by pipe B as 'b'.

Given the provided data, when pipe A operates from 2 PM to 10 PM (8 hours) and pipe B operates from 3 PM to 10 PM (7 hours), the tank becomes completely filled. Thus, we have:

8a - 7b = 1 [1]

Also, according to the second scenario, when pipe A is open from 2 PM to 6 PM (4 hours) and pipe B operates for 2 hours (from 4 PM to 6 PM), the tank gets filled. This leads to:

4a - 2b = 1 [2]

By multiplying equation [2] and subtracting [1] from it, we obtain:

8a - 4b - (8a - 7b) = 2 - 1

This simplifies to:

7b - 4b = 1

Which means: b = $\frac{1}{3}$

Substituting the value of b into equation [2], we get:

$4a - 2(\frac{1}{3}) = 1$

This simplifies to:

$4a -\frac{ 2}{3} = 1$

So: $4a = 1 + \frac{2}{3}$

Which leads to: $a = \frac{5}{12}$

Hence, the filling rate is $\frac{5}{12}.$

If only pipe A is operational, and the tank gets filled in 'n' hours, we have the equation:

$n \times a = 1$

Substituting the value of a:

$n \times (\frac{5}{12}) = 1$

This simplifies to: $n = \frac{12}{5}$

So, n = 2.4 hours or 144 minutes.