In what time would a cistern be filled by three pipes whose diameters are 1 cm, 1 1/3 cm and 2 cm running… · ABC26GN3399
Subject: General Aptitude · Chapter: Pipes and Cisterns · Exam: Railways 2006
In what time would a cistern be filled by three pipes whose diameters are 1 cm, $1 \frac{1}{3}$ cm and 2 cm running together, when the largest alone will fill it in 61 minutes, the amount of water flowing in by each pipe, being proportional to the square of its diameter?
(a)25 minutes
(b)30 minutes
(c)36 minutes
(d)40 minutes
Answer
Answer (as printed): C
Explanation
Let t1, t2 and t3 be the times taken by pipes with diameters 4 1 cm, cm and 2 cm respectively. 3 PIPES AND CISTERNS Since time taken to fill the tank is inversely proportional to the amount of water flowing through it, we have 1 k k t3 ∝ 2 or t3 = 2 ⇒ 61 = ⇒ k = 244. r r 4 k k 9 549 Thus, t1 = = 244; t2 = = × 244 = . (1)2 4 2 16 4 3 1 1 4 Net part filled in 1 min = + + 244 61 549 1 1 4 1 9 + 36 + 16 = + 1 + = 61 4 9 61 36 1 61 1 = × = . 61 36 36 Hence, all the three pipes together would fill the tank in 36 minutes.
Explanation as extracted from the printed page; notation may be imperfect.