(Rates) Time and Work

Hi, Sjas31,

Can you please elaborate the last step.

New hours required - 12/7.2 = 1.67 or (5/3).

Regards,
Raxit T.

This is the way I approach.
12 is the total manhours required to finish a job. Hence, the new 7.2 Men will take - 12/7.2 hours to finish the same job.

Hello Akrati,

The Unitary method is probably the best method to solve this question on Rates.

Let the total work done be 1 unit. Since 6 men can do 1 unit in 2 hours, it means that they work at the rate of ½ units per hour. This means that every man can work at the rate of \(\frac{1}{12}\) units per hour.

Working at this rate, 9 men can do ¾ units per hour. But, the question mentions that the group of 9 men work at \(\frac{4}{5}\)th of the capacity (rate) of the 6-member group. This means that 9 men can do \(\frac{4}{5} * \frac{(3}{4)}\) = \frac{3}{5} units per hour.

When work is constant, time and rate are reciprocal of each other.

In this question, we have taken the work as 1 unit, which means we have kept it constant. For this work, the rate of 9 men is \(\frac{3}{5}\) units per hour. Therefore, the time taken to complete the entire work will be the reciprocal of \(\frac{3}{5}\) i.e. \(\frac{5}{3}\) hours.

The correct answer option is D.

Hope that helps!