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The volume of water flowing through a pipe is directly proportional to square of it’s radius. A tank has four inlet pipes with diameters as 2 cm, 4 cm, 6 cm and 8 cm. If the smallest pipe, alone, can fill a tank in 30 hours, then how much time would all the four pipes, when working together would take?
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- 1 hour
- 4 hours
- 6 hours
- None of these
- 1 hour
Correct Option: A
We are given that V = k (r)²
where V is volume of water and ‘r’ is radius of pipe and K is a constant.
| The smallest pipe takes 30 hours to fill the tank alone, hence work done in 1 hour = | ||
| 30 |
| radius = | = | = 1 | ||
| 2 | 2 |
| = k( 1 )² so, k = | ||
| 30 | 30 |
| Work done in 1 hour by Pipe 2 = |  |  | ² | = | |||
| 30 | 2 | 30 |
| Work done in 1 hour by Pipe 3 = | | | ² | = | |||
| 30 | 2 | 30 |
| Work done in 1 hour by Pipe 4 = | | | ² | = | |||
| 30 | 2 | 30 |
| In 1 hour, work done by all 4 pipes = | + | + | + | = | = 1 | |||||
| 30 | 30 | 30 | 30 | 30 |
Hence, the whole tank gets filled in 1 hour.
