In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2

Similar question was given to me on my job interview in a management consulting firm! Oksana, you are great!

OK, let's go on to the solution:

12 X 6 -> 20, X - ?

9(former) 20 7.5 -> 10 <=> 6(latter) 20 7.5 -> 10 => (12/6)*(X/20)*(6/7.5) = 20/10 => X = 25.

25 days.

OK, pakoo. Look, 9 former workers do the same job as 6 latter workers ceteris paribus (in the same # of hours, same # of days), because their productivities relate to each other at a ratio of 3:2.

Then 6 "productive" workers make 10 TV sets in 20 days of 7.5 hours/day.

How many TV sets would make 12 "productive" workers in 20 days working 6 hours/day?

Number of TV sets depends on

a) time in days(positively),

b) duration of each working day(positively),

=> total productivity ~ WORKERS*DAYS*HOURS. (here "~" means "is proportional to")

We know that 10 ~ 6*20*7.5

And we know that 20 ~ 12*DAYS*6.

=> dividing first by the second we get DAYS = 25.

It is 20 *(9/12) * (7.5/6) *(20/10)*(2/3) = 25 days

here we can use mandays formula.

M1D1H1/W1=M2D2H2/W2.

M1=9,D1=20,D1=15/2, W1=10.

IN second case, efficiency of 2men latter equals 3men of former.
so here 12 men becomes 2/3=12/M2 = > M2=18, D2 =X, H2= 6, W2=20


9*20*15/2 /10=18*x*6/20

x=25

Basically we can do it by total man-hours.

10 TV sets take 9*20*7.5 hours
-> 10 TV sets take 1350 hours
-> 1 TV sets take 135 hours

Now, 20 TV sets will take 20*135 hours = 2700 hours
Since 12 persons are working 6 hours per day, they put up a combined 72 hours every day.

So, total days = 2700/72 = 300/8 = 37.5 days

But since in this case, 2 people work as much as 3 people, they would take 2/3rd of the time.

So, actual days = (2/3)*37.5 = 25

The ans has to be 25 days.
I will try to do it by simple logic.
We know first, 9 men can assemble 10 TV sets in 20 days working 71/2 hours daily i.e. 150 hrs in total.
So, 9M can assemble 10 TV sets in 150 hrs.
We can say, 9M can assemble 1 TV set in 150/10=15 hrs.
Thus, 1M can assemble 1 TV set in 15X9= 135 hrs.

Now, we know 2M of latter are equivalent to 3M of former.
So if 1 M can assemble 1 TV set in 135 hrs, so 3M can do it in 135/3= 45 hrs.
This is equivalent to 2M of latter. Hence, 2M of latter case now can assemble 1 TV set in 45 hrs.
Or, 1M of latter case can assemble 1 TV set in 45X2= 90 hrs.

Now, 1 M of latter case can assemble 20 TV sets in 90X20 hrs.
Also, 12 M will take much lesser time than 1 M. So, 12 M will do the work in (90X20)/12 hrs.
We are asked to find out the no of days if they work 6 hrs daily.
So, the no of days will be (90X20)/(12X6).
This comes out be 25 DAYS.

if 9 workers can do 10 tv sets in 20 days (working 7.5 hours each day) then:

10= 9(X) *150; where (X) is the rate of work and 150 is 20 days * 7.5 hours a day. Solving this equation X=1/135

Since the problem states that 2 workers do as much as 3 workers in the first set, we have that: (3*1/135)/2, which is equal to 1/90 (the new rate of work.

Finally, solving for 20 sets and 6 hours worked each day, we will have the following equation:

20= [12*(1/90)] *[D*6], where [12*(1/90)] is the rate of work for 12 people and D is the number of D worked. Solving this equation we have that D=1800/72= 25

The question seems slightly heavy because of the number of data points given. Let me simplify it by presenting a stepwise detailed solution

Given
We 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.

Approach
We 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 Out
First set of people

Work 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 people

Work 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

Hi karishma,

Can you please explain how you got (20/10) in the above expression?

In the former case, they assemble 10 tv sets and in the latter case they assemble 20 tv sets. Since they assemble more tv's in the second case, days taken will be more so we multiply previous days taken (20) by 20/10.

Here's my approach -

Efficiency of 9 former men = 6 latter men
=> 6 latter men make 10 sets in 150 hours
=> 12 latter men make 20 sets in 150 hours = 25 days (Considering 6 hour/day)

Is this right ?

- to assemble 20 tv it will take 20/(8/135) = 168.75 hours


I kept getting 337.5 as the answer here.

The questions involving multiple variables in work rate can usually be done in a single step.

But before we solve here, let's make people in the two cases comparable.
2 people of latter equivalent to 3 people of former.
12 people of latter equivalent to 18 people of former.

So in case 1 there were 9 people and in case 2 there were 18 equivalent people

"In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?"

9 people ........10 tv sets.........20 days............7.5 hrs
18 people........20 tv sets.........?? days .............6 hrs

We start with the unknown - the number of days.
The number of days will change. They will become 20 * (9/18) * (20/10) * (7.5/6) = 25 days

20 is the original number of days which needs to be adjusted to factor in the changes in the variables.

You multiply it by 9/18 because when number of people changes from 9 to 18, the number of days will decrease. So you multiply by a number less than 1.
You multiply by 20/10 because when number of tv sets increase from 10 to 20, number of days will increase. So you multiply by a number more than 1.
You multiply by 7.5/6 because when number of hours decrease from 7.5 to 6, number of days required will increase. So you multiply by a number more than 1.

Using this logic, you don't have to worry about how each variable varies with the other. Just use the logic of increase/decrease and less than 1/more than 1.

In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50

I was pressed for time(I almost took 3.5 min), So I have to make a quick guess nonetheless I will give both the approaches - quick guess and detailed.
Quick guess:

9 persons took = 20(\(\frac{15}{2}\)) hours
9 guys ---- 10tv sets ---- 150 hrs
12 guys--- 20 tv sets ----- ???? should be "<300" i.e \(\frac{300}{6}\) = must be <50 days

3 guys are extra -- \(\frac{150}{3}\) = 50 hrs , substract from 300 -50 => 250 hrs => \(\frac{250}{6}\) = approx. 25

Semi Detail approach:

we already worked out first two steps .

9 guys ---- 10tv sets ---- 150 hrs => Efficiency per head = \(\frac{1}{15*9}\) = \(\frac{1}{135}\)
12 guys--- 20 tv sets ----- ???? should be "<300" i.e \(\frac{300}{6}\) = must be <50 days

3 guys from 12 are equivalent to 2 guys out of 9, so remove 1 from 12, you should calculate for 11 workers.

=(11*\(\frac{1}{135}\)) * (x) = 20 tv sets (remember that the efficiency is apprxly correct, you are good as long as the options are not very narrow)
=> x = approx 25


"Kudos will encourage me, don't mind to give me one if my answer helped you"

Please find the solution as attached

­The last line in this problem is extremely vital to find out the efficiency of persons who will assemble 20 TV sets.

Previously, 2 people's work = now, 3 people's work.
Therefore, previously 12 people's work = now, (12*3)/2 = 18 people's work.

We know, work=people*hours*days
So, 10/(20*7.5*9)=20/(6*18*D) where D=number of days required to assemble 20 tv sets by 12 persons.
or D=(20*20*7.5*9)/(10*6*8)=25 days. Option (D) is correct.