Quantitative Aptitude Ques 2006

Question: Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?

Options:

A) 51 min 12 s

B) 52 min 1 s

C) 48 min 15 s

D) 55 min

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, radius of pipe $ \frac{5}{2\times 10}=\frac{5}{20}cm $ $ [\because 1cm=10mm] $ Height of pipe $ =1000cm $ Radius of vessel $ =20cm $ and height $ =24cm $ Volume of water flow in one minute from cylindrical pipe $ =\pi {{( \frac{5}{20} )}^{2}}\times 1000=\frac{125}{2}\pi cm^{3} $ and volume of conical vessel $ =\frac{1}{3}\pi {{(20)}^{2}}\times 24=3200\pi cm^{3} $

$ \therefore $ Required time $ =\frac{3200\pi \times 2}{125\pi }=51\frac{1}{5} $ or $ 51\min 12s $

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