Quote:
In what time would a cistern be filled by three pipes whose diameters are 1 cm , 4/3 cm, 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 square of its diameter ??
A. 18 minutes
B. 20 minutes
C. 40 minutes
D. 36 minutes
E. 72 minutes.
\((d_1)^2*(time_1)=(d_2)^2*(time_2)…time_1=61\)
\((2)^2*(61)=(1)^2*(time_2)…4(61)=(time_2)…time_2=244\)
\((2)^2*(61)=(4/3)^2*(time_2)…4(61)(9)/16=(time_3)…time_3=549/4\)
\(rate_n=\frac{1.cistern}{time_n}\)
\(\frac{1.cistern}{add.rates}=time.to.fill\)
\(time.to.fill=\frac{1}{1/61+1/244+1/549/4}=\frac{1}{5/244+4/549}=\frac{1}{5/(4*61)+4/(9*61)}=\frac{61}{5/4+4/9}=36\)
Answer (D)