Aptitude - Chain Rule - Discussion

Discussion :: Chain Rule - General Questions (Q.No.1)

1. 

3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

[A]. 9
[B]. 10
[C]. 11
[D]. 12

Answer: Option D

Explanation:

Let the required number of working hours per day be x.

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

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

Pumps 4 : 3 :: 8 : x
Days 1 : 2

4 x 1 x x = 3 x 2 x 8

x = (3 x 2 x 8)
(4)

x = 12.


Guri said: (Oct 29, 2010)  
I didn't get how you have solved it. Can you explain me this all step by step?

Shaunak said: (Nov 28, 2010)  
It's simple direct and inverse ratio theory. You can apply unitary method,but that'll take a hell lot of time.

Sivakumar said: (Nov 30, 2010)  
a:b::c:d=>bc=ad

Math Master said: (Dec 31, 2010)  
Better you do like this:
3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 4 pumps then
48/4=12 hrs.

Anil said: (Jan 18, 2011)  
That's the better way of explaining.

Mehar said: (Feb 2, 2011)  
D P H
2 3 8 ==> Fill the tank
1 4 x ==> Have to do empty same tank ,
so work is same then
2*3*8=1*4*x => x=12.

Vishal said: (Feb 2, 2011)  
3 pumb work in 2 days = 16 hours for empty the tank
1 pump work in 2 days = 16*3 = 48 hours for empty the tank
so 4 pump ...........= (16*3)/4 = 12..

Uttam said: (Feb 5, 2011)  
@ Math Master

Your approach is good, but it dint use the case that pumps should empty the tank within 1 day, is it doesn't make any difference?

Miss Mathphobia said: (Mar 30, 2011)  
I liked MathMaster's method...quite simple and easy 2 understand...

Ganesh said: (Apr 7, 2011)  
Mehar. Your Explanation is very easy.

Abhishek said: (Apr 19, 2011)  
@ Math Master I like your Approach :))

Bernard said: (Jun 2, 2011)  
4 x 1 x x = 3 x 2 x 8

x = (3 x 2 x 8) / (4)

x = 12.

Akhilesh Sahu said: (Jul 12, 2011)  
Please solve my problem

If 38 men , working 6 hours a day ,can do a piece of work in 12 days , find the number of days in which 57 men working 8 hours a day, can do twice that piece of work, supposing that two men of the first set do as much work in 1 hour as 3 men of the secand set do in 3/2 hours.

Umesh said: (Jul 28, 2011)  
Total work (Time to empty the tank by one pump) = 3(pumps)* 8(hours)*2(days)
= 42hours

When 4 pumps are using it will take 42/4= 12 hours

Anamika said: (Aug 8, 2011)  
Math Master's solution is really easy to uderstand

Cauverypithan said: (Aug 8, 2011)  
Math master method is wrong if 3 pumps works a day for 16 hour and one pump will 16/3 not 16*3.

Naresh said: (Aug 15, 2011)  
Thanks mehar.

Hiscan said: (Aug 28, 2011)  
@Cauverypithan
Math master is rite....coz 3 pumps will empty in 16hrs....
if they r using one pump,then work load ll increase,then 48hrs is rite....
still not clear...
then c...3 pump ll empty one tank in 16hr...so more the no of pump faster it gets emptied,
lesser the no of pump slower it gets emptied...

Deepika said: (Sep 17, 2011)  
Thanks for all for there short cuts.

Imraz said: (Sep 25, 2011)  
3 pumps 8 hours 2 days =work
3*8*2=work----->eqn1

now to complete the same work with 4 pumps in 1 day how many hours are required? lets take the hours required as x. then we can write the same work as

4 pump x hours 1 day =work

4*x*1=work ---->eqn2

equating both equation
3*8*2=4*x*1
x=48/4
x=12 hours

Raja said: (Oct 5, 2011)  
@maher. I am just asking where is the concept of chain rule (indirect propprtion) approach.

Sudheer said: (Oct 5, 2011)  
Imraz said well.

Yogendra said: (Dec 15, 2011)  
Thanks imraz your method is very easy to understand.

Maths Lover said: (Dec 22, 2011)  
@math master and all.

Your approach is right because fortunately question is asking of 1 day. If not. Then we have to divide the answer by number of days. So people take care of that also.

Kuntal Paul said: (Dec 28, 2011)  
Mathmaster method is so simple and effective.

Ram Chowdary M said: (Feb 6, 2012)  
Math master really thank you sir your said easy and simple method.

Hari said: (Mar 9, 2012)  
Yes it's very easy to understand solved by Mathmaster. ThanQ.

I can't understand your question Mr. Akhilesh sahu.

Sanjit said: (Mar 18, 2012)  
As a lay man I liked the DPH formula of meher.

Thanks.

Sandeep said: (Apr 1, 2012)  
GIVEN: 3 pumps' 1 hour's work= 1/16
SOLUTION : 1 pump's 1 hour's work= 1/48
4 pumps' 1 hour's work= (1/48)*4 = 1/12
hence 4 pumps will finish the work in 12 hours

Kartik said: (May 23, 2012)  
Thanks to mathmaster.

Ravi Teja P said: (Jun 17, 2012)  
Let pumps - 'p', no.of hrs/day - 'h', no.of days - 'd'.

For this type of problems, first know what we have to find? here we have to find hrs/day i.e. 'h'.

Now, find out the relation of 'h' with other parameters 'p' and 'd'.

If no.of pumps increases, no.of hrs/day decreases (inverse proportion).

p & (1/h). (1) **Assume &-proportionality symbol**.

If no.of days increases, no.of hrs/day decreases (inverse proportion).

d & (1/h). (2).

From (1) & (2).

pd & (1/h). (3).

=> pdh=constant.

=> p1*d1*h1=p2*d2*h2.

=> 3*2*8=4*1*x.

=> x=12.

Aara said: (Oct 11, 2012)  
Why this formula given below does not work with this question but works with other such similar questions?

(Machine (1) x Time) /Work = (Machine (2) x Time) /Work.

Ashish And Amartya said: (Oct 13, 2012)  
We found a new method.
step 1- calc the total time for 3 pumps ie(2*8)
2- now for 1 pump time=(2*8)*3
3- " " 4 pump time = ((2*8)*3)/4..ans.

Simple said: (Oct 21, 2012)  
(Machine (1) x Time) /Work = (Machine (2) x Time) /Work.

This formula works here also
3 * 8(hrs)* 2(day) /1 =4 * x(hrs) * 1(day)/1
==> x= 12

Here work done is 1 since full tank is to be emptied.

Hanumanth said: (Dec 15, 2012)  
pumps*days*hours=pumps*days*hours.

4*1*x=3*8*2.

x=12.

That's simple

Naveen Moorthy said: (Feb 27, 2013)  
As tank are Same.

So 3x8=24 hours required for 1 day for that tank.

So hrs will be same.

For 4 tanks, 4x6=24 for 2 days.

If it 1 day, 6x2=12 hours.

Shubhank said: (Jul 30, 2013)  
Can anyone just explain the chain rule with direct and indirect proportion?

Lakshmi said: (Aug 2, 2013)  
3 pumps -> 8h -> 2 days.

4 pumps -> ? -> 1 day.

3*8*2/4*1 = 12.

Vivek said: (Aug 16, 2013)  
One pump requires 16 *3 = 48 hrs to empty the tank.

4 pump requires 48/4 = 12 hrs.

Sobuz said: (Oct 3, 2013)  
At First we find the Total_hour to finish the work, that is:

3*8*2 = 48.

So, 4*X*1 = 48.

X = 48/4 = 12.

Deepika said: (Oct 21, 2013)  
Hey I have one simple way that is ma formula is n*D*H/w = N1*D1*H1/W1.

Where n = no.of men.
d = days.
h = hours.
w = work.

So my opinion is 3*8*2 = 4*1*x.

x = 12.

Karm Bodh Yadav said: (Jan 7, 2014)  
There is simple and understandable style to solve:

3 pumps take 24 hrs total (8 Hrs a day).

If 1 pump will be working then, it will need 8*3 = 24 hrs.

1 pump need 24 Hrs in two day.

1 pump need 24*2 Hrs in one day.

If I contribute 4 pumps then.

48/4 = 12 hrs.

Celita Lewis said: (Jan 15, 2014)  
If 3 pumps work for 8 hours than total hours in 1 day is 3 * 8 = 24 hours.

So in 2 days total hours of work is 48 hours.

So for 4 pumps the work distributed is (48 / 4) = 12 hours.

Arjita said: (Apr 12, 2014)  
@Math master: I didn't get your first statement.

Emilia said: (Nov 22, 2014)  
I like @Mehar's Method. So simple to understand. Thanks.

Rajeev Guda said: (Dec 15, 2014)  
3*8 = 24 hours in 2 day i.e., 12 hours a day with 3 pumps.

How can it be 12 hours with 4 pumps?

Ankita Agrawal said: (Jan 15, 2015)  
Its so simple. Just we need to apply correct logic.

Neha said: (Jul 19, 2015)  
Why are you 16*3 for 1 pump?

Nikhilkuruli said: (Jul 21, 2015)  
@Akhilesh sahu: 27 hours.

Ekta Ravish said: (Aug 26, 2015)  
Its very much easy to solve question using these pattern.

Kjkj Tikhir said: (Oct 17, 2015)  
3 pumps = 8 hrs/day.

1 pump = 8*3 = 24 hrs/day and 48 hrs in 2 days.

Considering 1 day work of 3 pumps we know that 24/3 = 8.

Now f we consider 1 day work of 4 pumps should not it be 24/4 = 6.

Please anyone, why? are we considering for two days when it is asked for 1 day work?

Smit said: (Oct 20, 2015)  
I can't understand please explain.

Manasi said: (Apr 18, 2016)  
Thanks for solving the problem. It helps always.

Ankit said: (Jul 7, 2016)  
Math master's solution is great.

Babar said: (Oct 27, 2016)  
3 pumps working 8 hours.
So total hours = 3 * 8 = 24 * 2 = 48 to fill.
So can empty 48/4 = 12 hours.
Then, the answer = 12.

Haruthra said: (Dec 18, 2016)  
I got the solution by this method.

3 : 16 = 4 : x.
so,
3/4 = x / 16
4x = 64
x = 12.

Therefore, the answer is 12 hours.

Sanskriti said: (Mar 15, 2017)  
Working 8 hours a day, 12 people can do a piece of work in 15 days. How many people will complete the same work in 16 days working 9 hours a day?

Please solve the problem.

Suhani said: (Mar 16, 2017)  
8 hours * 12 people * 15 days = work;
Let, x people will complete the work in 16 days so-
9 hours * x people * 16 days = work,
8 * 12 * 15 = 9 * x * 16,
x = 10 people.

Akojenu Felix said: (May 11, 2017)  
Maths Master Really Explained It Well. I Need More Of Your Teaching.

Monika said: (Sep 27, 2017)  
Please solve my problem.

1200 men 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

Azar- Benz said: (Nov 14, 2017)  
This question is asked for my interview in Mercedes Benz.

Mohamed said: (Mar 8, 2018)  
If 38 men, working 6 hours a day, can do a piece of work in 12 days, find the number of days in which 57 men working 8 hours a day, can do twice that piece of work, supposing that two men of the first set do as much work in 1 hour as 3 men of the second set do in 3/2 hours whats the answer for this?

Can Anyone answer for this?

Shivam Mehta said: (Jul 26, 2019)  
There is a direct formula m1d1t1w2= m2d2t2w1,
where m1,m2 = no of men case 1,2.
w1,w2= work done in case 1,2.
d1,d2= no of days in case 1,2.
t1,t2= no of hours in case 1,2.

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