Aptitude - Chain Rule - Discussion

@subhi.

12 men completes a piece of work in 66 days.
=> Work done by 12men/day = (1/66)th part.
=> Work done by 1man/day = (1/66*12)= (1/792)th part.

Similarly,
15 women completes the work in 66 days.
=> Work done by 15women/day = (1/66)th part.
=> Work done by 1women/day = (1/66*15)= (1/990)th part.

Now.. 24men and 3women together.
So, calculate work done by (24men and 3women)/day.
=> (24/792)+(3/990)
=> (1/33)+(1/330)
=> (11/330) = 1/30.

=> Work done by (24men and 3women)/day= (1/30)th part.
=> Total no.of days to complete the work is 30 days.

I always solve this as a work and time problem:
39 people working 5 hours a day finished 1/12th the work in 1 day.
39 people will therefore finish 1/60th (1/12 x 1/5) the work in 1 hour.
1 person will finish (1/60 x 1/39)th the work in 1 hour
So 30 people working for 6 hours will finish:
(1/60) x (1/39) x 6 x 30 = everything cancels out and you are left with 1/13th.
So: 30 people working for 6 hours will finish 1/13th the work in a day meaning they will take 13 days to finish.

39 persons ---> 5 hrs per day ---> 1 work ---> 12 days.

1 person ---> 5 hrs per day ---> 1 work ---> 12 x 39 days.

1 person ---> 1 hr per day ---> 1 work ---> 12 x 39 x 5 days.

30 persons ---> 1 hr per day ---> 1 work ---> 12 x 39 x 5/30 days.

30 persons ---> 6 hrs per day ---> 1 work ---> 12 x 39 x 5/(30 x 6) days.

30 persons ---> 6 hrs per day ---> 1 work ---> 13 days.

39 person 1 day work is ---> 1/12.
39 person complete total work in 1/12 * 1/5.
1person complete in 1/12 * 1/5 * 1 * 39 ---> eq1.

Similarly
30 person one day work let be n.
So they take 1/n.
Total time 1/n * 1/6hour.
1person one day work 1/30 * 1/n * 1/6 ---> eq2.


Person efficiency are same so,
Equation 1 = eqution2.
Calculate value of n will obtain.

I thing the easy way to solve this out is below.

39 12 5

30 x 6

after cross multiplication, we will have

39 1

3 x

According to rule
39x = 3
x = 3 / 39

now due to indirect relation we will change the above equation as::: x = 39/3 which results ===13

Thanks

For this type of Q, we can simply use an LCM Method.

Take LCM of 39 or 30 =390 this is total time of work that we calculate after that 39 works for 12 Day..but we calculate individuals work so simply divide 390/39=10 unit.

And we need to find how many days 30 workers taken to complete this work so 390/30=13 unit 13 unit is the answer.

Here 39 men work for 5 * 12 hrs totally to complete the road.

Let x be the no of days that 30 people work, then the no of hours 30 people take to complete road is 6x hours.

The amount of work done is inversely proportional to no. of working hours.
i.e
(39/30) = (6x/60).
x = 13.

Hope you understand.

There is simple formula for this type of questions:

M1D1H1 M2D2H2
------ = ------
W1 W2

Where,

M = No.of Men
D = No.of Days
H = No.of Hours
W = Amt of Work done.

In this problem, if we apply this equation,

39*12*5 = 30*6*x

x=13 is the answer.

The equation is 30 x 6 x x = 39 x 5 x 12 not clear to understand.

Please explain it clearly. When I solved this problem I got equation as 39 x 12 x 5 = 30 x x x 6.

How come you got that equation?

Hope you all understand....

First codition=total hours to complete the work=39 persons * 12 days * 5 hr

Second codition=total hours to complete the work=30 persons * x days * 6 hr

since the work is still the same so
39*12*5=30*x*6
x=13