Aptitude - Chain Rule - Discussion

Discussion :: Chain Rule - General Questions (Q.No.5)

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 B

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: (Aug 21, 2010)  
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: (Oct 14, 2010)  
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: (Oct 28, 2010)  
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: (Jan 18, 2011)  
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: (Jul 9, 2011)  
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: (Aug 26, 2011)  
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: (Dec 26, 2011)  
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.

Subhi said: (May 25, 2012)  
I have a question plz answer:

12 men or 15 women completes a piece of work in 66 days, 24 men and 3 women together can complete in in how many days?

Ravi Teja P said: (Jun 17, 2012)  
@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.

Sachin Prakash Srivastava said: (Jul 25, 2012)  
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.

H.R said: (Dec 15, 2012)  
@Anila.

Persons*days*hours = Persons*days*hours.

Aranya said: (Mar 22, 2013)  
Persons 30 : 39 :: 12 : x.

Working hours/day 6 : 5.

How did we get the following line?

30 x 6 x x = 39 x 5 x 12.

Mithilesh said: (Aug 30, 2013)  
1 person can do this work in 39*12*5 = 2340 hrs.

Hence 30 persons will do in 2340/30 = 78 hrs = 78/6 13 days.

I think its very understandable.

Raja said: (Oct 23, 2013)  
The total number of hours of work is 39(people)*60 (Working 60 hours) = 2340.

Now 30 people working 6 hours so the number of days are 2340/180 = 13.

Nisha said: (May 16, 2014)  
The sum of infinity of a geometric series is 60. If its first term is 80, find the common ratio? can you give the answers?

Lipu said: (Sep 20, 2014)  
39 persons can repair in 60 hours.

1 person can do in 60*39 hours.

30 persons can do it in(60*39)/30 hours = 78 hours.

If they work 6 hours a day.
So no.of days is 78/6 = 13 days.

Buddhika said: (Dec 31, 2014)  
M1D1H1 = M2D2H2

39*12*5 = 30*D*6.
2340 = 180d.
13 = d.

Sukumar Satyen said: (Apr 16, 2015)  
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.

Appu said: (Mar 10, 2016)  
39*12*5 = 2340.

30*x*6 = 2340.

x = 2340/180 = 13.

Santosh K said: (Mar 21, 2016)  
For the first statement Total man hours = 39*12*5.

Again for the second statement man hours = 30*X*6.

Equating both equation X = 39*12*5/30*X*6 = 13 days.

Nilesh Tripathi said: (May 8, 2016)  
@Pratswinz.

You explained it in the best way. Thanks, it's very helpful.

Pavan Power Star Fan said: (Jul 22, 2016)  
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.

Sanjay said: (Nov 7, 2016)  
You have taken this as:
Persons --> 30 : 39 :: 12 : x,
Working hours/day --> 6 : 5,

Why it can't be like,
Persons --> 39 : 30 :: 12 : x,
Working hours/day --> 5 : 6,
So, I get the equation as (39 * 5 * x) = (30 * 6 * 12).

Vaibhav said: (Nov 7, 2016)  
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.

Nagendra Kumbar said: (Nov 21, 2016)  
1st section = 39 P *12 D *5H
2nd section =30 P * X D * 6H

Then ,
39 * 12 * 5 = 30 * X * 6,
X = (39 * 12 * 5)/(30 * 6),
X = 13.

Suman said: (Feb 25, 2017)  
If 6 man or 8 woman can repair a road in 28 days. How long 8 man and 2 woman will repair it.

Please solve this.

Tushar Waghchaure said: (Jul 4, 2017)  
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.

Vivek Singh said: (Sep 18, 2018)  
Thank you all for explaining the solution.

Lavanya said: (Sep 28, 2018)  
There is a formula. Here it is a total person(M) * days(D) * hours(H):
M1 * D1 * H1=M2 * D2 * H2.

Lokesh said: (Sep 13, 2019)  
30 x 12 x 5 = 2340.
30 x days x 6 = 2340 (because work is same),
180xdays = 2340,
Days = 13.

Nikita said: (Feb 1, 2020)  
Can someone please explain the calculation in detail?

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