A cistern is filled in 30 minutes by three pipes A, B and C. The pipe C is thrice as fast as pipe A and pipe B is twice as fast as A. The time taken by A alone to fill the cistern is :

180 minutes

The correct answer is Option (1) → 180 minutes

Work Done per minute by A = $\frac{1}{x}$

Work done per minute by B = $\frac{2}{x}$

Work done per minute by C = $\frac{3}{x}$

$⇒\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{1}{30}$

$⇒\frac{6}{x}=\frac{1}{30}$

$⇒x=180$ minutes