Wrong answer and solution: (Question:852342.0)

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kamlesh kumar

· started a discussion

· 1 Months ago

Wrong answer and solution: (Question:852342.0)

When outlet pipe C takes 9*4=36 hrs to empty and inlet pipe A takes 9*3=27 hrs to fill the tank than a filled tank will never be emptied by A and C working simultaneously.
Please correct it.

Question:

Pipe A takes ¾ of the times required by pipe B to fill the empty tank individually. When an outlet pipe C is also opened simultaneously with pipe A and pipe B. it takes 3/4 more time to fill the empty tank than it takes, when only pipe A and pipe B are opened together if it takes to fill 27 hours when all the three pipes are opened simultaneously, then in what time pipe A and pipe C can fill the full tank operating together.

Options:

180 hrs

108 hrs

201 hrs

None of these

Solution:

Let pipe A fill the tank in 3x hr. then pipe B fill it in 4x hr.

Therefore, in 1 hr. they will fill = $\frac{1}{3 x} + \frac{1}{4 x} = \frac{7}{12 x}$

So, they will take $\frac{12 x}{7}$ hrs.

When an outlet pipe C is also opened then it takes

= $\frac{12 x}{7} + \frac{12 x}{7} \times \frac{3}{4}$

= $\frac{12 x}{7} + \frac{9 x}{7}$ = 3x hr.

Now, In one hr. pipe A, B and C working together fill = $\frac{1}{3 x} + \frac{1}{4 x} - \frac{1}{c} = \frac{1}{3 x}$

$\frac{1}{c} = \frac{7}{12 x} - \frac{1}{3 x}$

C = 4x

Hence, In 4x hours pipe C can empty the whole tank.

Now, since 3x = 27, x = 9 hrs.

so, A alone can fill the whole tank in 27 hr. and C can alone empty the tank in 36 hr.

so, required time = $1/(1/27-1/36) = 1/1/108 =108hr.$

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Wrong answer and solution: (Question:852342.0)

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