# Consider the below-given statements and the question. You have to decide whether the data provided in the statements are sufficient to answer the ques

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Consider the below-given statements and the question. You have to decide whether the data provided in the statements are sufficient to answer the question.

Three pipes named Pipe A, Pipe B and Pipe C is there to fill a tank. How much time it will take to fill the tank if all the three pipes opened together?

Statement I: If opened Pipe A and Pipe B together to fill the tank, it will take 10 hours.

Statement II: It will take 12 hours to fill the tank if both Pipe B and Pipe C opened together.

Statement III: It will take 15 hours to fill the tank if both Pipe A and Pipe C opened together.

1. The data in statement I alone is sufficeint to answer the question, while the data in statement II and statement III is not sufficient to answer the question.
2. The data in statement II alone is sufficeint to answer the question, while the data in statement I and statement III is not sufficient to answer the question.
3. The data in all the statements I, II and III together is not sufficient to answer the question.
4. The data in all the statements I, II and III are necessary to answer the question.

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Correct Answer - Option 4 : The data in all the statements I, II and III are necessary to answer the question.

Time taken to fill the tank if all three pipes are opened together can be calculated by the following equation

$\frac {1}{Time \hspace{1mm}taken} =\frac {1}{A} +\frac {1}{B} +\frac {1}{C}$

From Statement I

$\frac {1}{A} +\frac {1}{B} =\frac {1}{10}$      ---(1)

Value of C is not given  ⇒ ∴ statement I alone can't provide the answer

From Statement II

$\frac {1}{B} +\frac {1}{C} =\frac {1}{12}$      ---(2)

Value of A is not given  ⇒ ∴ statement II alone can't provide the answer

From Statement III

$\frac {1}{A} +\frac {1}{C} =\frac {1}{15}$      ---(3)

Value of B is not given  ⇒ ∴ statement II alone can't provide the answer

Considering all the statements

Adding all equations (.i.e (1) + (2) + (3) ) gives,

$\frac {2}{A} +\frac {2}{B} + \frac {2}{C}=\frac {1}{10}+\frac {1}{12}+\frac {1}{15}$

⇒  $\frac {1}{A} +\frac {1}{B} + \frac {1}{C}=\frac {15}{120}=\frac {1}{8}$

It will take 8 hours to fill the tank if all three pipes are opened together.

All three statements are necessary to answer the question.