Discussion

Explanation:

We know, efficiency of a pipe ∝ cross-section

and, cross-section ∝ (radius)²

⇒ efficiency ∝ (radius)²

∴ $\frac{efficiency of bigger pipe}{efficiency of smaller pipe}$ = $\frac{radius of bigger pipe}{radius of smaller pipe}$ = $\frac{4}{1}$

Also, Time ∝ 1/efficiency

⇒ $\frac{Time taken by bigger pipe}{Time taken by smaller pipe}$ = $\frac{efficiency of smaller pipe}{efficiency of bigger pipe}$

⇒ 60/x = 1/4 

⇒ x = 240 minutes

Now, when they work together time taken to fill the tank = $\frac{1}{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$60$}\right.}+{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$240$}\right.}}$ = 48 minutes.

Hence, option (d).

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