CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and work. This questions combines the idea of time and work with proportions. Note: Look closely at the proportionalities

Question 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. 253.125
2. \\frac{100}{163}\\)
3. \\frac{25}{256}\\)
4. \\frac{16}{29}\\)

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Look closely at the proportionalities

G α No of workers²
G α √(No. of Machines)
G α No of hours
200 α 4² * √4 * 8
200 α 16 * 2 * 8
200 α 256
200 = k x 256
K = \\frac{200}{256}\\)
K = \\frac{25}{32}\\)
When 3 people work for 12 hours each with 9 machines, the number of goods that will be produced is equal to \\frac{25}{32}\\) * 3² * √9 * 12 = 253.125

The question is "When 3 people work for 12 hours each with 9 machines, how many goods will be produced?"

Hence, the answer is "253.125".

Choice A is the correct answer.