# CAT Practice : Pipes cisterns, Work time

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Look closely at the proportionalities

## Pipes Cisterns - Work Time

Q.12: Number of units of a good that can be produced by a factory is directly proportional to the square of the number of workers, square root of the number of machines and to the number of hours put in. The factory produces 200 goods when 4 people work for 8 hours each with 4 machines. When 3 people work for 12 hours each with 9 machines, how many goods will be produced?.
1. ${K = \frac{25}{32}}$
2. ${K = \frac{100}{163}}$
3. ${K = \frac{25}{256}}$
4. ${K = \frac{16}{29}}$

Choice A. ${K = \frac{25}{32}}$

## Detailed Solution

G α No of workers2
G α $\sqrt{No. of Machines}$
G α No of hours 200 α $4^{2} \times \sqrt{4} \times 8$
200 α 16 x 2 x 8
200 α 256
200 = k x 256
${K = \frac{200}{256}}$

${K = \frac{25}{32}}$

Correct Answer: ${K = \frac{25}{32}}$

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## More questions from Pipes Cisterns, Work Time

Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.