Aptitude - Time and Work - Discussion

2. 

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

[A].

9 1 days
5

[B].

9 2 days
5

[C].

9 3 days
5

[D]. 10

Answer: Option C

Explanation:

(A + B + C)'s 1 day's work = 1 ,
4

A's 1 day's work = 1 ,
16

B's 1 day's work = 1 .
12

Therefore C's 1 day's work = 1 - ( 1 + 1 ) = ( 1 - 7 ) = 5 .
4 16 12 4 48 48

So, C alone can do the work in 48 = 9 3 days.
5 5


Amit said: (Jan 2, 2011)  
How the fractional 7/48 arrived?

Gurjit said: (Jan 2, 2011)  
Why did you write 5/48 as 48/5 ?

Aparna said: (Jan 2, 2011)  
@amit

First solve the bracket,
it is
(1/16+1/12)

First method:

Simply you can do cross multiplication
we get
(12+16)/12*16
after solving we get
7/48

Second method:

Find the lcm of denominators
that's of 12 and 16
It is 48,and multiply it with each fractions
i:e
we get
(3+4)/48

Aparna said: (Jan 2, 2011)  
@gurjit
as per formula,
If A's 1 day's work = 1/n , then A can finish the work in n days.
here also same
c's one days work=5/48
hence he can complete whole work in 48/5 days,tats asked to us

and remember any fraction can also be written in
quotient*remainder/divisor format
when solved 48/5
quotient=9
remainder=3
divisor=5
hence,
9*3/5

Bharathi said: (Jan 6, 2011)  
How should know A, B, C work is 1/4.

Geetha said: (Jan 6, 2011)  
@Bharathi

In ques they have mentioned that
with the help of C they did the job in 4 days
thatsy A+B+C=1/4

Sowjanya said: (Jan 14, 2011)  
Thanks geeta you solved my doubt.

Reema said: (Jan 16, 2011)  
How did 5/48 come explain it?

Naresh Kumar said: (Jan 18, 2011)  
Thanks Aparna and Geetha. You have solved my doubt also.

I am very poor in solving such types of question.

Shantanu said: (Jan 19, 2011)  
Reema
look
A's 1 day's work = 1/16
because he took 16 days to complete the task

similarly
C's 1 day's work =5/48
so total no. of days will be 48/5

Uthappa.U.K said: (Jan 20, 2011)  
1/4-7/48 cannot be equal to 5/48. Can anyone explain this to me?

Jagan said: (Jan 25, 2011)  
@ Uthappa

1/4-7/48 = ((48*1)-(7*4))/(4*48) //cross multiplication

=(48-28)/192 = 20/192 //ok........ now its divisible by 4

=5/48 // r u got it?

Neelam said: (Feb 2, 2011)  
Thanks uthaap, I was confused about the cross multiplication. Now you explained in easy manner.

Dinesk said: (Feb 8, 2011)  
Nice aparna.

Sathya said: (Feb 19, 2011)  
@Shantanu.

Your explain is very short and very sweet.

Shalu said: (Mar 11, 2011)  
@Aparna

Why you substracted 1/4 -7/48 why dont you add 1/4+7/48 ?

Sagar said: (Mar 19, 2011)  
@SHALU
SUPPOSE A,B,C ARE HAVING 10 RUPIEES
WE KNOW DAT A=5 AND B=3 NW WE HAVE TO FIND C
THEN WE WILL ADD BOTH A AND B AND REMOVE FRM TOTAL HERE ALSO SAME WE HAD DONE
UNDERSTOOD

Nalini said: (Mar 27, 2011)  
@reema

take lcm of 1/4 - 7/48
i..e

12-7/48
= 5/48:)
got it??

Mallik said: (Apr 30, 2011)  
Reema explained clearly.

Nikita said: (Jun 15, 2011)  
1/4= 1/12+1/16+1/c
1/4-7/48=1/c
c=9*3/5


1/c= c's one day work

Sunil said: (Jul 17, 2011)  
Why 48/5 is written? please help me.

Sunaina said: (Jul 20, 2011)  
Why we should take 16 and 12 as 1/16 and 1/12?

Karthick said: (Jul 22, 2011)  
Why the fraction 5/48 is changed to 48/5?

Shimpi said: (Jul 28, 2011)  
Please help me in 1/4-7/48.

Srikanth said: (Aug 5, 2011)  
How 48/5 is written as 9*3/5 ?

Sowmya said: (Aug 5, 2011)  
@Srikanth

9*3/5=(9*5)+3=48/5

Ravi said: (Aug 6, 2011)  
Thanks uththapa. I get it.

Saquib Ali said: (Aug 19, 2011)  
You can solve all these sums very fast...

a can do the work in 16 days
b can do the work in 12 days
c can do the work in x days

Calc LCM of 16, 12 and x = 48x

units of work in a day by a = 48x/16 = 3x units
units of work in a day by b = 48x/12 = 4x units
units of work in a day by a = 48x/16 = 48 units

Total units of work in a day = 3x + 4x + 48= 7x+48
Thus in 4 days = 4(7x+48)= 28x+192

Total units of work=48x

Thus,
28x+192=48x
20x=192
x=9 3/5 days.

Meenakshi Dhawan said: (Sep 21, 2011)  
@Saquib Ali.

You have solved it wisely.

Ovii said: (Sep 25, 2011)  
@aparna

Little help to the explanation of 1's days work.

If A's 1 day work = 1/n than the complete/whole work can be done in n*1 days.

It can be modify to above 1 day's work, e.g

if A's 5 days work = 1/25, than the complete/whole work = 5*25= 125.

Simran said: (Oct 17, 2011)  
Thanks for the help.

Vasudevarao said: (Nov 17, 2011)  
Thank you nikitha well s. C method thanku.

Swetha said: (Nov 26, 2011)  
1/12+1/16
=4+3/48
=7/48

Chandrakant said: (Dec 14, 2011)  
Wan we do it this way?

A=16days B=12days, and A+B+C=4 days
So 16+12+C = 4
i.e; 28-4 = c
Hence c = 24days

NOTE: Pls tell me if this method is correct, if not then why?

Indian said: (Dec 21, 2011)  
@ Ovii

Thanks for explanation, Now I understood well.

Tiny said: (Jan 15, 2012)  
@chandrakant.

Your method is totaly wrong. When c comes in right hand side it will become negative.

Udita said: (Jan 21, 2012)  
@Saquib Ali.

Please explain the following step.

Units of work in a day by a = 48x/16 = 48 units.

Amrut said: (Mar 19, 2012)  
C s one day work is 5/48. But how you came to 48/5, I mean C finish job in 48/5 days. Is there any formula for this result?

Anshu said: (Mar 31, 2012)  
"A" can do the 1/16 of the work in a day.
"B" can do the 1/12 of the work in a day.
A + b + c = 1/4 of the work.
1/16 + 1/12 + c = 1/4.
3/48 + 4/ 48 + c = 1/4.
7/48 + c = 1/4.
C = 1/4 - 7/48 = 12-7/48 = 5/48.
C can do 5/48 of the work per day.
Therefore he can complete his work on 48/5 days = 9 3/5.

Rajasekar said: (Apr 4, 2012)  
How 5/48 is written 48/5?

Suryakiran Varma said: (May 8, 2012)  
Look,
A can do a work in 16 days,so his one day work will be=1/16
and also B's one day work will be =1/12;
in the same way A,B,C together do a work in 4 days,so thier one day work will be=1/4
C 's one day work will be=(A+B+C)'s one day work - (A+B)'s one day work
i.e..
=(1/4)-(1/16+1/12)
=(1/4)-(7/48)
=(5/48)
thus,C's one day work is = 5/48,
so,he can do the work in 48/5 days..i.e..9 3/5.

Hiren said: (Jun 8, 2012)  
Why you write 48/5 from 5/48.

Amit.J said: (Jun 19, 2012)  
A+B+C=4 day.
A=16 day.
B=12 day.
C=?

Formula..

A+B+C=A*B*C/AB+BC+CA

4=192C/192+28C

4(192+28C)=192C

768+112C=192C

768=192C-112C

768=80C

768/80=C

C=48/5 Ans.

Parthasarathy said: (Jun 20, 2012)  
@HIREN.

If A can do some work in N days.

So A can do that same work in one day =1/N.

So the answer 5/48 obtained by (1/4) - (1/16+1/4) =5/48.

So you should consider this as only 48/5.

Pradeep said: (Jun 23, 2012)  
Thank you aparna.

Kalai said: (Aug 23, 2012)  
I can't understand how 5/48 becomes 48/5. Can you clarify for me.

Shiyamala said: (Aug 29, 2012)  
A=1/16;
B=1/12;
A+B=[1/16+1/12]
=[16+12/192]{1/16*12/12=16/192;1/12*16/16=16/192)
=28/192
=7/48 {4*7=28; 48*4=192)
C-[A+B]=1/4-7/48 {1/4*12/12=12/48)
=12-7/48
=5/48
but c work alone.so,48/5=9*3/5

Ajay Jabalpur said: (Oct 7, 2012)  
@Hiren.

If A's one day work = 1/n, then A can finish the work in n/1 days.

Similarly,

C's one day work is 5/48, then C can finish the work in 48/5 days.

Twinkle said: (Jan 19, 2013)  
A+B+C=1/4.

[1/16]+[1/12]+C=[1/4].

C=0.1041.

THEREFORE, 1/0.1041=48/5.

i.e: 9*3/5.

Sudha said: (Mar 9, 2013)  
At the end of explanation,

C's 1 day work is 5/48 I calculated up to to this but how it comes work in 48/5 days.
Because acc. to formula if A's 1 day work is 1/n' then A can finish work in n' days.
Means only it comes 48. I am just confuse. please explain me.

Srinivas said: (Mar 27, 2013)  
If I go for another way as follows:

A B and C can do work in 4days.

A alone 16 days.
B alone 12 days.

C alone ?... Lets assume it as X.

Let me apply this formula
Work done by A B and C put together i.e 4= (16*12*X)/(16+12+X) //(A*B*C)/(A+B+C).


28+X=48X.
28=47X.

X=28/47.

According To you Answer is Wrong How is it. Please Reply me As soon As possible.

Sonu said: (Mar 30, 2013)  
Why do we take fraction and add and subtract everything?

Ashim Ray said: (May 23, 2013)  
Why you have shown in the last fraction 48/5 in where the result has come out 5/48?

Manoj Kumar said: (Jun 8, 2013)  
Why you have shown in the last fraction 48/5 in where the result has come out 5/48? Please explain it.

Leena said: (Jun 20, 2013)  
One day's work is 5/48.

But we want number of days that 'C' alone can do, so 48/5 days.

Shakir said: (Jun 27, 2013)  
We know a formula that,

If A do a work in X days, B do a work in Y days and C do a work in Z days.
Then all of three can do the same work in = XYZ/(XY+YZ+ZX).

Then,
According to question,

A do a work in 16 days,B do the same work in 12 days and let C do the same work in Days
Then we can write as,

(16*12*x)/(16*12+12x+16x) = 4.

And solve it.

Sunny said: (Jun 28, 2013)  
How to convert 5/48 = 9*3/5?

Srinivas said: (Jul 4, 2013)  
C's 1 day work was 5/48. So it can be written as 1/(48/5) and as per the formula if C can do a work in 1/n days then C can complete work in n days which is 48/5. Mixed fraction is written as 9(3/5) = (5*9+3 )/5.

Carlo said: (Jul 26, 2013)  
1/4 = 1/16 + 1/12 + 1/X.

X = 9.6 days or 9 3/5 days.

Naseer Mohammad said: (Aug 6, 2013)  
Why you have shown 48/5 instead of 5/48? Any one can help me.

Sonyy said: (Aug 6, 2013)  
Why you have shown 48/5 instead of 5/48? Anyone can help me.

Sona said: (Aug 6, 2013)  
Hey I understood they gave answer in fraction form so 5/48 we need not any fraction so its inverse 48/5.

C = 1/4 = 5/48.

C = 4 = 48/5.

Anusha said: (Aug 8, 2013)  
I didn't get clearly that how 5/48 is reversed? can anyone help me for better understanding?

Dumpati Mahesh said: (Aug 14, 2013)  
@Anusha,

For getting one day work it should be reversed. i.e. 1/(5/48) = 48/5.

Dumapti Mahesh said: (Aug 14, 2013)  
I have another method to solve this:

Suppose the C's work take as z days.

We have the formula that (A+B+C) work = (xyz/(xy+yz+zx)).

Here x=12(A alone work),y=16(B alone work).

=>192z/(192+16z+12z)=4 days(given).

upon simplifying. we get,

48z = 192+28z.

z = 192/20=> 48/5.

Hasan Ali Tariq said: (Sep 15, 2013)  
@Carlo.

I think Carlo explain it nicely and simply. The issue of inverse value 5/48 to 48/5.

Chethan K M said: (Sep 20, 2013)  
How to write 48/5 in the form of 9 3/5?

Jeevi said: (Sep 20, 2013)  
The 5 is base and 5 table 9*5=45 remain 3 so you should write 9 3/5 are you understand.

Surendra said: (Sep 28, 2013)  
Why you have shown 48/5 instead of 5/48?

Sagar Malunjkar said: (Oct 3, 2013)  
@Surendra.
See carefully,

In second last step we have calculated C's 1days work is 5/48.

But our exact question is "C alone can do the job in how much days" so according to formula -

If C's 1 day's work = 1/n, then C can finish the work in n days ie n/1 days.

So that's why 5/48 became 48/5.

Shakti said: (Dec 7, 2013)  
Let total work = 48.

Then A effi. = 3, b = 4 and find C effi. as (7+n)*4 = 48.

It comes 5.

Hence divide 48 by 5 and get your answer.

Khan said: (Dec 17, 2013)  
A's 1 day work is 1/16.

B's 1 day work is 1/12. As given.

That means C's 5 days work is 5/48 na?

Jansi said: (Dec 26, 2013)  
Hello Mr. Khan,

You can refer June -19th tuesday Mr. Amit.J has explained good. He given clear explanation.

But Mr.Amit you had used this formula, (a+b+c) = a*b*c/ (ab+bc+ca). Always we can use this formula or any other restriction is there. Can you explain me?

Vamsi said: (Jan 8, 2014)  
LCM of numbers 16, 12, 4 = 48.

16 is 3 times.
12 is 4 times.
4 is 12 times.
a-16d-3 units.
b-12d-4 units.
c-?- ? units.

a+b+c = 12 units .

Total work complete 12 units.
a+b complete 7.
Remaining work c 5.
= total/remaining work, 48/5 = 9.6 this is also written 9 3/5.

Arun Kumar Arui said: (Jan 19, 2014)  
A+B+C = 1/4.
1/16+1/12+1/x = 1/4.
(1/16+1/12-1/4) = -1/x.

Taking lcm.
-5/48 = -1/x.

cross multiplying,
-5x = -48.
x = 48/5.
x = 9 3/5.

Raga said: (Mar 9, 2014)  
Why 5/48 concert to 48/5 please clarify me?

Des said: (Mar 10, 2014)  
How did they get 48 in 7/48?

Kaustav said: (Mar 16, 2014)  
One step equation:1/16+1/12+1/x=1/4.

Amruta said: (Apr 5, 2014)  
Amruta here,

Lets see this simple method,
Lcm of 16 and 12 is 48.

So A and B will finish their work in 3 and 4 hr.
Answer C will finish in 12 hr.

Hence 12- (3+4) = 5 hr.

Hence answer is 48/5.

Prachi said: (Jun 10, 2014)  
Can you explain me why 5/48 reverse?

Aditya said: (Jun 16, 2014)  
'A' work in 16 days.

Working of 'A' in one day is 1/16.

Similarly working of 'C' in one day is 5/48.

So 'C' work finished.

Guri said: (Jul 2, 2014)  
@Aparna.

LCM. Method is the best shortcut but expect common sense more than you have.

Aaja said: (Jul 8, 2014)  
Hi,

How to convert decimal to fraction?

Dushyant Verma said: (Jul 9, 2014)  
In 4 days.

A --> 25%
B --> 33 %
C --> 100-25-33 = 42 %

42% work done in 4 days then,

100% ---------- (4/42)*100 = 9(3/5).

Happy Singh said: (Jul 16, 2014)  
Easy method in step by step :

Given values :
A=1/16, b=1/12.
(A+B+C)'S 1 day's work = 1/4.

So we can write,
(A+B+c)=1/4.
(1/16+1/12+C)=1/4.
C=(1/4-(1/16+1/12)).
C=(1/4-7/48).
C=(5/48).

C's one day work is = 5/48,
so, C can do the work in 48/5 days.

Yogesh Sayam said: (Aug 2, 2014)  
How calculate answer is 5/48?

Yogesh Sayam said: (Aug 2, 2014)  
5/48 calculation is:

1/4-7/48 is cross multiplication.
28-48/192 = 20/192 (divided by 2) .
= 10/96 Answer is 5/48.

Rekha said: (Aug 2, 2014)  
How this 9 3/5 is got from 5/48?

Soumyajit said: (Aug 3, 2014)  
If I want to solve this problem in this way,
Suppose C can do this work in X day.
Then, in 1 day A can do 1/16, B can do 1/12, C can do 1/X.
Then, 1/16 + 1/12 + 1/X = 1/4.

Can I solved this answer in this way?

Naim Hussain said: (Aug 7, 2014)  
For those who can't understand the 5/48 and 48/5 issue, here's my explanation:

C can do 5/48 amount of work in = 1 day.
C can do 1 full work in = 1/5/48 = 48/5 days.

Hope this helps for good.

Kishore said: (Aug 12, 2014)  
How can we know the that C can do full in (1/how much work 'C ' done in one day) ?

Raj said: (Sep 4, 2014)  
Why did write 48/5 is in 5/48?

Yasodha said: (Sep 23, 2014)  
How to came 4/48 explain it?

Rajesh said: (Oct 1, 2014)  
Please explain:

1/4-7/48 = 5/48.

5/48 how it comes?

Suresh said: (Oct 7, 2014)  
LCM of 4 & 48 is 48.

So 1/4-7/48 = (12*1-7*1)/48.
= 5/48.

Deepika said: (Nov 6, 2014)  
How is last step is taken 5/48 is reversed to 48/5?

Soumya said: (Dec 2, 2014)  
@Deepika.

C's 1 day work is 5/48.
Here we require C's total work.

Total work should be taken as '1'.

So, 1 day work i.e,5/48*number of days used to complete the work(unknown, so take it as 'x') = total work 1.

Simply, 5/48*x = 1.
5x = 48.
x = 48/5.

So C's total work is 48/5.

Ankit said: (Dec 18, 2014)  
How to change this 5/48 to 48/5?

Abi said: (Dec 19, 2014)  
A can do work in 16 days.

Then, A's 1 day work = 1/16.

Meanwhile, C's 1 day work = 5/48 (our ans).

Then, C can do work in 48/5 days.

Emma said: (Jan 8, 2015)  
Where does 48 come from in this come equation?

Harmit said: (Feb 6, 2015)  
Easiest method.

LCM is 48 of 16 &12. Then A can complete work in 3 work and B can 4 work.

Now A B C can complete 12 work.

Now A and B complete 7 work so still remaining work is 5.

So C can alone complete work 48/5. So answer is C. You can easily calculate.

Sasmita said: (Feb 9, 2015)  
Tell me any one that c's work. I can't understand it.

Gautam said: (Feb 25, 2015)  
Answer of C work 5/48 to 48/5.

This is one day work of C.

Example as given in question itself.

A work complete in 16 day so in 1 day 'a' will complete 1/16 portion of whole work. Whole work completed by a is 16/1=16 days.

Naresh said: (Feb 28, 2015)  
How do you get 1/4?

Pundir said: (Mar 6, 2015)  
All the explanations are really amazing and understandable. But I would like to add a point to the discussion. Why did we do 1/16, 1/12 or 1/4. See there is lot frequency distribution in the values. So to ease our lives we want to compare all this to a benchmark value.

In this case everybody is taking different number of duration's to complete a particular task. So first we want to find out how much work everybody was able to complete in any particular day. Just to make the calculations easier.

And if one can do (1/16)th part of a work in one day, then just by reversing the fraction we can get to know in total how many days he/she will be able to complete the entire task.

Hope this will help.

Mahesh Sawant said: (Mar 11, 2015)  
Please explain how come 5/48?

Mohammed Aqib said: (Apr 8, 2015)  
In equation 5/48 how did 5 arise?

Anurag said: (Apr 25, 2015)  
Can anybody explain LCM method like this?

Lets see this simple method,

LCM of 16 and 12 is 48.

So A and B will finish their work in 3 and 4 hr.

Answer C will finish in 12 hr.

Hence 12-(3+4) = 5 hr.

Hence answer is 48/5.

Ayush said: (May 12, 2015)  
Can anybody explain the basic to know how the 48/5 comes?

Phani Kumar said: (May 16, 2015)  
Can explain 5/48 has come?

Lokesh said: (May 18, 2015)  
Why C-A+B?

Therefore C's 1 day's work = (1/4)-(1/16+1/20).

Ravikumar said: (Jun 5, 2015)  
How (1/16+1/20)?

Jack said: (Jun 17, 2015)  
B's 1 day's work = 1/12.

Therefore C's 1 day's work = 1-(1+1) = (1 -7) = 5.

4 16 12 4 48 48.

So, C alone can do the work in 48 = 93 days.

Lovely said: (Jul 17, 2015)  
Why take 1/4 in first step?

Ramakrishna said: (Jul 19, 2015)  
@RaviKumar.

We have A+C = 4 -->A+C 1 day work = 1/4.

B+C = 4 --> B+C 1 day work = 1/4.

We add (A+C)+(B+C) = (1/4)+(1/4).

A+B+2C = (4+4)/(4*4) = 8/16 = 1/2.
A+B+2C = 1/2.
A+B+C = 1/(2*2) = 1/4.

That's it A+B+C = 1/4 -->A+B+C's 1 day work.

A's 1 day work = 1/16.
B's 1 day work = 1/12.
C's 1 day work = "We have A+B+C's 1 day work then subtraction to(A's 1 day+B's 1 day)".

= (A+B+C)-(A+B).
= (1/4)-(1/16+1/12).
= 1/4-(7/48) = 5/48.

C's 1 day work= 5/48 then C can do job= 48/5.

= Formula :: X 1 day task 1/n, x can do task n;

=48/5---> (9*5)+3/5---> 9 3/5.
=9 3/5.

Suersh said: (Jul 26, 2015)  
How 9 3/5?

Adusumalli Prasanna said: (Jul 28, 2015)  
a+b+c=1/4 a's 1st day work = 1/16 b's 1st day work = 1/12.

Therefore c's 1 day work = 1/4-{1/16+1/12) after that 1/4-(12+16/192) {by doing LCM) by dividing 28/192 (by multiplying 2nd table) then we get 1/4-7/48 (by doing LCM).

We get (48-28/192) = 20/192 = 10/96 (dividing with 2 table) we get 5/48. Now please help me why we are taking as 48/5.

Whats the reason explain me clearly please?

Shivu said: (Aug 12, 2015)  
Hi thanks all of you solving this problem in easy methods.

Helper said: (Aug 13, 2015)  
We get 1/x=5/48.

Then we want x. So x=48/5.

Bhavana said: (Aug 20, 2015)  
Firstly take the LCM.

A B ABC.
16 12 4.

LCM IS 48 then ratio is.

A B ABC.
3 4 12.

If a+b-ABC then it's find the value of C = 5 total is 48.

Then divide the 48/5 so simple.

Naresh Saini said: (Aug 24, 2015)  
How it is possible to write 5/48 to 48/5?

Khizer said: (Sep 6, 2015)  
= 1/16+1/12+1/C = 1/4.

C = 48/5.

Lijin said: (Sep 12, 2015)  
How it possible to write 5/48 to 48/5?

See A can complete a work in n days.

A's 1 day work = 1/n.

So here 1/n = 5/48.

So n = 48/5.

Got it!

Tamilmani said: (Sep 18, 2015)  
Please answer sir basic formula applied please.

Sagar said: (Oct 5, 2015)  
Anyone explain me what is 5 and 48 in relation to C?

Onkar Vitthal Dabhole said: (Oct 30, 2015)  
A very very simple solution than the provided as above.

A can complete a work in 16 days, B can complete the same work in 12 days and with the help of C together if they complete the work in 4 days, so assume total work to be done is 48. (LCM of 16, 12, 4).

Persons A B C | A+B+C.

Days- 16 12x = (48/5) = (9+3/5)4.

Work/day- 3 4 5 12 = 3+4+C.

Hence C = 5.

----------------------------------------------------------------.

Work - 48 48 48 48.

Abhishek said: (Nov 5, 2015)  
A - 16 days | 3 unit/day

L. C. M of (16, 12, 4).

| | = 48.

B - 12 days |4 unit/day|.

| |.

C - ? |x unit/day|.

-------------------------------------------------.

(A+B+C) - 4 days | 12 unit/day |.

So, for C we get (12-3+4) = 5 unit/day.

If C can do 5 unit in 1 day, then 48 unit can be done in 48/5 = 9*3/5 days.

Guys this is the easiest way.

Dikesh said: (Nov 25, 2015)  
Hi all,

If we convert 5/48 can lead to decimal, normally we won't measure days of decimal, hence we have to reverse it simple that's it. I think all you guys understood this.

Kumar said: (Dec 26, 2015)  
@Amit.

It is addition.

Prachi said: (Jan 12, 2016)  
Like a b c are doing work in four days then can we assume the approach like it.

1/16 + 1/12+x = 4.

So x = 41/48, work of c.

Please tell.

Ganesh said: (Jan 22, 2016)  
Total work is 48 units.

A can do work in 16 days.

It means A completes 3 units per day.

B can do work in 12 days.

It means B completes 4 units per day.

Now A and B is helped by C and completed work in 4 days.

It means A, B and C together doing 12 units per day.

It means A+B+C = 12.

Sub A and B values.

3+4+C = 12.

C = 5.

It means C completes 5 units per day.

For 48 units?

Answer: 48/5.

Mathivanan said: (Feb 10, 2016)  
Awesome answers the way of explaining is very excellent. Thank you all of you.

Sidhartha said: (Apr 17, 2016)  
How it come 5/48? Please give a clear solution.

Sudhanshu Patra said: (May 21, 2016)  
@Ganesh.

Thanks for explaining the answer.

Sankalp said: (Jun 4, 2016)  
Hi, I have a doubt. Please clarify it.

After finding LCM why do we reverse the answer? (i.e why do we have 48/5 after getting LCM as 5/48).

Shweta Narkhede said: (Jul 11, 2016)  
Thank you very much friends, I got lots of help because of yours discussion with this topic.

Amogh said: (Sep 17, 2016)  
A can complete 1/16th of the work in 1 day.

B can complete 1/12th of the work in 1 day.

Let C complete 1/Xth of the work in 1 day.

So, A, B & C can complete (1/16 + 1/12 + 1/X)th part of the work in 1 day.

Therefore in 4 days, they together can complete = 4*(1/16 + 1/12 + 1/X)th part of the work . Always remember & denote work completed as 1.

On solving 4*(1/16 + 1/12 + 1/X) = 1, you can get the value of x which is the number of days taken by C to do the work.

Hope it helps you.

Sunny said: (Sep 19, 2016)  
A's efficiency = 3, and B's efficiency =4, so (3 + 4) = 5 then C's efficiency (12 - 7) =5, So total work take LCM of (16, 12, 4) = 48, so C alone finished the work 48/5.

Asshok007 said: (Oct 29, 2016)  
@Shantanu

Thank you, you are right.

Actually, A can solve in 16 days for one day it will be 1/16. if we take for 2 days work it will become 2/16. in the same way the work done by c per day is 5/48. If you want total work done by 'c' just reverse the fraction like 48/5.

Ex: THE TOTAL WORK DONE BY 'B' IS IN 12DAYS, FOR ONE DAY 12,IN THE SCENE 12/1. You should remember that 5/48 is the work done by 'c' in one day.

Lakshmi said: (Nov 23, 2016)  
Thanks for clarifying the solution @Ajay.

Ishwar Shrestha said: (Feb 6, 2017)  
Guys don't be confused.

A can do in 16 days.
B can do in 12 days.
A B & C can do in 4 days.

So,
Total work is to be done is 48.
( lcm of all)
Then A's efficiency is 3.
B's effc is 4.
A B n C effc is 12.
So, A + B + C = 12
4 + 3 + C = 12
7 + c = 12
C = 5.

Then 5/48 or 48/5.

Shruti said: (Mar 30, 2017)  
I didn't get still that how 5/48 came from 28/192, actually, I don't know the basics to solve maths so please explain.

Ammu said: (Apr 1, 2017)  
@Shruti.

A's one day work = 1/16.
B's one day work = 1/12.
with the help of C , they finished in 4 days.
So, A+B+C=4 days,
Therefore, (A+B+C)'s one day work = 1/4.
If C alone is = X.
then 1/16+1/12+X = 1/4,
X= 1/4-(1/16+1/12) {Lcm of 16, 12 is 48 and by the cross multiplication will get 7/48}
= 1/4-7/48,
= 12-7/48,
= 5/48,
C's one day work = 5/48.

Lokesh said: (Apr 3, 2017)  
How is possible at 5/48 write 48/5? please solve it for me.

Gokul said: (Apr 23, 2017)  
According to me,
a+b+c=4
a=16
b=12
c=?

C = a * b/b-c,
=16 * 12/16-12,
= 16 * 12/4,
=4 * 12 = 48.

Am I correct?

Jamshed Alam said: (May 8, 2017)  
A = 16 Days.
B = 12 Days.
A+B+C = 4 Days.
C = ?
1st of all we take LCM of 16, 12, and 4.
LCM of 16,12 and 4 is 48.
It means whole work is 48 unit then we find the unit of per day of all.
A = 48/16 = 3unit/day.
B = 48/12 = 4unit/day.
A+B+C = 48/4 = 12unit/day.
A+B = 3+4 = 7unit/day.

Now subtract from (A+B+C)-(A+B)=12-7 = 5.
C = 5unit/day.
It means C can alone of whole work is 48/5 days.

Ankur said: (May 14, 2017)  
How 7/48 come from 1/16+1/12?

Please explain me.

Vinay said: (Jun 6, 2017)  
A = 1/16.
B = 1/12.
According to Qsn A + B + C = 1/4.
Add A, B values.
Here,
1/16 + 1/12 + C = 1/4,
C = 1/4 - 1/16 - 1/12,
= 5/48.

Total Days of C = 48/5.

Monu Monika said: (Jul 8, 2017)  
Work is inversely proportional to days 5/48 is the answer for work To convert it into days he changed 5/48 into 48/5.

Shafiyulla said: (Jul 31, 2017)  
Solve my doubt, please.

A+b+c=1/4 correct.

Then how C' s one day work became 1/4?

Sasi said: (Sep 5, 2017)  
A+b+c-(a+b)=1/4-1/16-1/12=1/4(1/1-1/4-1/3).
4*4**3=48.
=>12-7/48=5/48.

Amit Bhardwaj said: (Sep 27, 2017)  
Thanks, @Ishwar.

Anurag Singh said: (Oct 29, 2017)  
A work = 16 days.
B work = 12 days.

Total work done by A and B = 48 unit (LCM Of A and B).

So work done by A in one day = 48/16= 3 unit.
And work done by B in one day = 48/12 = 4 unit.

So work done by A and B in 1 day = 3+4 = 7 unit.
Work done by A and B in 4 days = 7*4 = 28 unit.

So remaining work = 48-28 = 20 unit.
So work done bye C in one day= 20/4 = 5 unit.

So total work done by C in days = 48/5 days =9*3/5 days.

Shivam Sharma said: (Nov 8, 2017)  
Help here, let's take c's work to be X then (1/16 + 1/12 + 1/X) = 1 but when I find for X by multiplying 4 inside of the bracket. I get a 80/11.

Ved Prakash Singh said: (Nov 29, 2017)  
A's one day work=1/16.
B's one day work=1/12.
Let C can finish the work in x days hence C's one day work=1/x.
A, B and C together can finish the work in 4 days and total work is 1.
4/16+4/12+4/x=1.
so x=48/5 =>9*3/5.

Manish said: (Jan 9, 2018)  
@ALL.

a&b's work for 4 days=7/12.
bal is c work =1-7/12=5/12.

c's 5/12 work in 4 days.

Therefore- 1 work ie 100 % work in how many days?
5/12 in 4 days.
1 in how many days.
4*12/5=48/5 days.
Fraction= 9*3/5.

Appu said: (Feb 8, 2018)  
Thanks @Aparna.

Vaishu said: (Mar 20, 2018)  
How did 1/4 become total one day's work?

Ritesh Raj said: (Apr 6, 2018)  
@All.

Check this;
A-16d
B-12d
C-xd.

Lcm of all 3=48x(let it be total work that they have to complete).
Now efficiency ( of A,B,C is 3x,4xand 48 resp)
Now. on 1st day all 3 together can do 3x+4x+48 works it is given that they together complete the work in 4 days so;

4*(3x+4x+48)=48 solve it get x, then you will get the answer.

Vikas said: (Apr 11, 2018)  
1/4-7/48= 5/48 how? Please explain.

Pavani said: (Apr 27, 2018)  
(A+B+C)'s efficiency - (A+B)'s efficiency = C's efficiency.
(1/4) - (1/16+1/12) = C's efficiency.
5/48 = C's efficiency.
So, the time taken, to complete the total work, by C = 48/5= 9 3/5.

Justine said: (Apr 28, 2018)  
How come that 48 gets retain? when you cross multiply 48/1 * 1/16 = 3 and 48/1 * 1/12 = 4?

Please explain me.

Imran said: (May 16, 2018)  
Can anyone explain me this question by LCM method?

Truptimayee Bahinipati said: (May 26, 2018)  
The solution in LCM method is;

Solution :
SUPPOSE TOTAL WORK=1UNIT.
A=15d L.C.M. of 15,20=60.
B=20d.
Then A=4.
B=3.
A+B=7unit=60.
4 unit=60/7*1/4=15/7day.
1day work of A+B=7/15unit.
Remaining work=1-7/15=8/15 unit left (Ans.)

Siba Siddquie said: (Jul 1, 2018)  
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:


LCm of A,B,A+B+C (16,12,4)=total work=48...;;
A' 1 day work=48/16=3;
same B=48/12=4..A+B+C=48/4=12,
A+B+C=12,
3+4+C=12,
C 'one day work =5,
total work is =48.

C completes the work in (days) = total work/one day work..(formula) = 48/5=9(3/5) => answer.

Jaga said: (Jul 4, 2018)  
Thanks @Aanurag.

Pooja said: (Jul 4, 2018)  
As per formula: If A completes 1/n work in 1 day then the days required by him to complete that 1 work alone will be 1 ÷ 1/n = n days.

Similarly, C can complete 5/48 part of the work in a day. To complete 1 work alone he will take 1 ÷ 5/48 days to 48/5.

Suchi said: (Jul 17, 2018)  
Thank you @Siba.

Aruva said: (Aug 13, 2018)  
Thank you @Soujanya.

Sunshine said: (Sep 3, 2018)  
A work = 16 days.
B work = 12 days.

Total work was done by A and B = 48 unit (LCM Of A and B).

So work done by A in one day = 48/16= 3 unit.
And work was done by B in one day = 48/12 = 4 unit.

So work done by A and B in 1 day = 3+4 = 7 unit.
Work was done by A and B in 4 days = 7*4 = 28 unit.

So remaining work = 48-28 = 20 unit.
So work done by C in one day= 20/4 = 5 unit.

So, the total work was done by C in days = 48/5 days =9*3/5 days.

Anish said: (Sep 24, 2018)  
@Sunshine.

In the question, it was mentioned that B and C can finish the work in 12 days not only A.
then how you can said B's work = 12 days?

Please explain the step.

Shivani said: (Nov 16, 2018)  
A can do the work = 16 days,
B can do the work =12days,
A+B+C together can do work =4 days.

let's take the LCM of 16,12 and 4 it is 48.
calculate the 1 day's work of A,B and A+B+C,
1day's work of A= 48/16= 3,
1day's work of B= 48/12= 4,
1day's work of A+B+C =48/4=12,
Here we calculate the 1day's work of c,
A+B+C=12,
3+4+C=12,
7+C=12,
C=12-7,
C=5.

Then,
c alone can do the work in;
C = 48/5 = 9 * 3/5 days.

Sai Kumar Reddy Nossam said: (Dec 9, 2018)  
common multiple for 12 and 16 is 48.

A's one day work =48/16=3 units,
B's one day work=48/12=4 units,
C's one day work??

A and B together do a piece of work in 4 days= 28 units.
remaining work ( C's work in 4 days)=48 - 20 =20 units,
C's work in one day=20/4=5 unit,
C alone can do the job in=(5 * 9)+3/5 = 9 3/5.

Shashi said: (Feb 23, 2019)  
A = 16.
B = 12.

Lcm for 16,12 is 48.
16*3 = 48.
12*4 = 48.

With the help of c they did the job in 4 days only,
So 48/4=12.
12-(a+b).
12-(3+4) = 5
Now 48/5 = 9.6 hrs.

Manoj Kumar Maharana said: (Jun 8, 2019)  
How come 5/48? Please explain.

Sai Naredla said: (Aug 13, 2019)  
A can do job in 16 days.
B can do in 12 days.

Make the LCM for both A and B.
After LCM we get 48.
This is the total work for both A and B=48.
For one day work of A is 16*3=48.

That means A can do 3 units of work per day,
For one day work of B is 12*4=48.

That means B can do 4 units of work per day.
(A+C)=3+4=7.
(B+C)=4+4=8.

TOTAL work of (A+B)and(B+C) = 7 + 8 = 15.

We find out c alone can do the job in how many days
So we can subtract 48-15=33.

Convert 33 in fraction form that you get the answer.

Sai Kumar said: (Aug 17, 2019)  
1/4- (1/16+1/12) = (1/4-7/48) please anyone explain this.

Shirisha said: (Aug 20, 2019)  
@Sai Kumar.

It is 1÷16 + 1÷12 so 1st do LCM of 16,12 then you'll get the answer as 48 later on divide (48÷16, 48÷12) then you'll get answers as 3 and 4 (as multiplied by the numerator 1 then 3*1 will be 3 and 4*1 will be 4) add 3+4 you'll get 7 then the final answer will be 7/48

Bhimesh said: (Sep 26, 2019)  
Why 5/48 is 48/5 because A can do work in 16 days so his efficiency for 1 day is 1/16.

(which means (work/time)). So same for C's 1-day work is 5/48 and he can complete the work in 48/5.

Sindhu said: (Oct 30, 2019)  
@Bhimesh.

Yes, you are correct.

Anup said: (Jan 23, 2020)  
16,12,4 of lcm=48.
16/48=3.
12/28=4.
4/48=12.


So, total works efficiency =12-7=5 per days;
48/5 is the answer.

Neha K. said: (Feb 19, 2020)  
I can't understand 9 3/5 last answer.

Vignesh said: (Apr 21, 2020)  
@Neha.

It is 48/5=> 45+3/5 = 9 * 3/5.

Sonu Singh said: (Jun 12, 2020)  
Thanks all for explaining.

Billal Hossain said: (Jul 13, 2020)  
Solution:

Let, C did the job in= x days.

ATQ,

1/16+ 1/12+ 1/x = 1/4.
=> 1/x= 1/4- 1/16-1/12,
=> 1/x= (12-3-4)/48,
=> 1/x= 5/48,
=> x= 48/5,
=> x = 9 (3/5).
C alone can do the job in 9(3/5) days.

Cherry said: (Aug 15, 2020)  
Good explanation, Thanks @Billal Hossain.

Chaitanya Galande said: (Sep 14, 2020)  
Consider A and B work alone.

1/16 + 1/12.
3/48 and 4/48.
That means A does work 3 units per day and B does 4 units per day.
So, now total work is done by A and B in one-day => 4 + 3 = 7 units per day
The total work is done by A and B in 4 days = 28 units.
Remaining units = 48-28 = 20 units.

That means 20 units work is done by C in 4 days in order to complete the work;
So, WORK DONE BY C IN ONE DAY = 20/4= 5 UNIT PER DAY,
C alone can do work in = 48/5 i.e 9(3/5).

Sana said: (Sep 28, 2020)  
Why the fraction is reciprocated at the end? Explain me, please.

Ishwar said: (Oct 2, 2020)  
Because time is inversely proportional to Rate and your calculated rate is 5/48 (this is C`s rate at which C working so).

Jeet said: (Dec 31, 2020)  
Take LCM of A and B.
The total work is 48.
A + B = 7 what should we add here so that work would complete in 4 days! So that number is 5.
3+4+5=12.

You can see they all can complete 48 works in 4 days. (48/12=4).
Therefore C's capacity is 5. When you'll divide the work by 5.
48/5 you'll get 9 3/5.

Sai said: (Jan 8, 2021)  
Answer is 9 3/5 days.

Karthick said: (Jan 27, 2021)  
How did come 5/48? Explain please.

Palem Ganesh said: (Feb 1, 2021)  
It's quite easy, I will tell the shortcut method.

Take LCM of 16 an 12 is 48 and;
Then find one day work as units.
A = 48/16 = 4.
B = 48/12 = 3.
C = ?.

We know they all together they take just 4 days.
Per day of 4 days work = 48/4 = 12.
A + B + C = 12.
4 + 3 + C = 12.
C = 5.
So, C can do work 5 units per day.
C= 48/5.

Jaya said: (Feb 3, 2021)  
Thank you friends.

Disha said: (Feb 21, 2021)  
5/48 of the whole work is done in one day. Then one whole work is;
5/48:1::1:x.
1*1/[5/48] = 48/5.

Gunjan said: (Aug 9, 2021)  
A-15.
B-20.

1/15 + 1/20 = 7/60.
7/60 x 4= 28/60 = 14/30 = 7/15.
( 1 - 7/15 ) = 8/15.

Gunjan said: (Aug 9, 2021)  
Agree @Truptimayee Bahinipati.

A=15 days.
B= 20 days.



Then the addition of 1/15 + 1/20 =7/60.

7/60 x 4 = 28/60, 28/60 = 14/30, 14/30 = 7/15.
[ 1- 7/15 ] = 8/15.
Answer = 8/15.

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