Question

3 pipes a b c can fill a tank in 6min 8 min and 12 min respectively. The pipe c is closed 6 min before the tank is filled. In what time will the tank be full

Answer 1

lcm of 6,8,12= 24

efficiency 4,3,2

6 min closed= 6*2=12

(24+12)/(4+3+2)

4

Answer 2

The tank will be full in 4 minutes

Solution:

Let the tank be full in x minutes

Given that,

A can fill the tank in 6 minutes

B can fill the tank in 8 minutes

C can fill the tank in 12 minutes

The pipe c is closed 6 min before the tank is filled

Then, we can say,

$\frac{x}{6} + \frac{x}{8} + \frac{x - 6}{12} = 1$

Solve the above,

$\frac{x \times 4}{6 \times 4} + \frac{x \times 3}{8 \times 3} + \frac{(x - 6) \times 2}{12 \times 2} = 1\\\\Simplify\\\\\frac{4x}{24} + \frac{3x}{24} + \frac{2x - 12}{24} = 1\\\\4x + 3x + 2x - 12 = 24\\\\Simplify\\\\9x = 12 + 24\\\\9x = 36\\\\x = 4$

Thus, the tank will be full in 4 minutes

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