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Aptitude - Chain Rule - Discussion

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"I never see what has been done; I only see what remains to be done."
- Marie Curie
5. 

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

[A]. 10[B]. 13
[C]. 14[D]. 15

Answer: Option A

Explanation:

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

More working hours per day, Less days (Indirect Proportion)

Persons 30 : 39 :: 12 : x
Working hours/day 6 : 5

30 x 6 x x = 39 x 5 x 12

x = (39 x 5 x 12)
(30 x 6)

x = 13.


Anila said: (Sat, Aug 21, 2010 01:40:49 PM)    
 
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?

Jeyan said: (Thu, Oct 14, 2010 09:41:15 PM)    
 
Ya. Right. Even I got so!

Why not we say 39 persons did work in (12*5) hours.

Then what would be 30 persons working for (x*6) hours ?

Rahul said: (Thu, Oct 28, 2010 03:46:12 AM)    
 
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.

Miyyapuram said: (Tue, Jan 18, 2011 01:46:38 PM)    
 
Ny cross multiplication method i didn't get correct ans.....
39---->12*5hrs
then 30---->x*6hrs

Now 30*12*5=39*x*6
then 30*12*5/39*6=x......... then i got 100/13........
is it correct or wrong

Pratswinz said: (Sat, Jul 9, 2011 12:18:18 PM)    
 
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

Adeel Jabbar said: (Fri, Aug 26, 2011 12:06:21 PM)    
 
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

Simha said: (Mon, Dec 26, 2011 03:18:40 PM)    
 
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.

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