The question seems slightly heavy because of the number of data points given. Let me simplify it by presenting a stepwise detailed solution
GivenWe are given information about two sets of people working. In the first case 9 people assemble 10 TV sets in 20 days working 7.5 hours/day. In the second case we are asked to find the time taken by 12 people to assemble 20 TV sets working 6 hours/day. We are also told that the amount of work done by 2 people in second case is equal to the amount of work done by 3 people in the first case.
Let's see how can we break down this question into simpler bits to get to our answer.
ApproachWe know that
Work = Rate * Time. For the first set of people we are given the amount of work done and the amount of time taken. We can use this information to find out the rate of work done by 1 person. For the next set of people we are given the amount of work to be done and are asked to find the time taken by them. For finding the time taken we will need the rate of work done by these people.
We are given a relation between the work done by the first set of people and the second set of people. We will use this information and the work rate equation to find out the rate of work done by second set of people and then the time taken by them to complete the work.
Working OutFirst set of peopleWork done by 9 people = 10 TV sets
Time taken by 9 people each = 7.5 hours for 20 days = \(20* 7.5\) hours
Rate of work done by 9 people = \(\frac{Work}{Time}\) = \(\frac{10}{20*7.5}\)
So, the rate of work done by 1 person \(= \frac{10}{20*7.5*9}\)
Second set of peopleWork done by 12 people = 20 TV sets
We are told that 2 people in the latter case do as much work as 3 people in the former. i.e.
work done by 2 persons in the second case = work done by 3 people in the first case.
Since time taken is the same, assuming \(R_{1}\) to be the rate of 1 person in the first case and \(R_{2}\) to be the rate of 1 person in the second case we can write
\(2 * R_{2} * t = 3 * R_{1} * t\) which gives us \(R_{2} = \frac{3}{2} * R_{1} = \frac{3}{2} * \frac{10}{20*7.5*9}\) for 1 person
Rate of work done by 12 people \(= 12 * \frac{3}{2} * \frac{10}{20*7.5*9}\)
Let's assume the number of days it took 12 people to assemble 20 TV sets be \(x\). As the people worked for 6 hours daily,time taken by 12 people each =\(6x\) hours.
Putting the above information in the equation Work = Rate * Time, we get
\(20 = 12 * \frac{3}{2} * \frac{10}{20*7.5*9} * 6x\)
\(x = 25\) days
Hope this helps
Regards
Harsh
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