Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 2)
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:

9 1 days
5

9 2 days
5

9 3 days
5

10
Answer: Option
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

Discussion:
224 comments Page 18 of 23.

Jamshed Alam said:   8 years ago
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:   8 years ago
How 7/48 come from 1/16+1/12?

Please explain me.

Vinay said:   8 years ago
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:   8 years ago
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:   8 years ago
Solve my doubt, please.

A+b+c=1/4 correct.

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

Sasi said:   8 years ago
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:   8 years ago
Thanks, @Ishwar.

Anurag Singh said:   8 years ago
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:   8 years ago
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:   8 years ago
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.


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