Question is wrong. (Question:852342.0)

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Ajay Sharma

· started a discussion

· 1 Months ago

Question is wrong. (Question:852342.0)

A's efficiency is more than C's. This means that A can fill the whole tank in 3x(or 27) hours while C can empty the whole tank in 4x(or 36) hours. Hence if both are opened together, then the tank would actually fill and it will not be emptied. Also time taken by both of them to fill the tank, will be found by dividing the Total Work by their combined efficiency. Please correct.

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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