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.