Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 7)
7.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Answer: Option
Explanation:
| A's 1 hour's work = | 1 | ; |
| 4 |
| (B + C)'s 1 hour's work = | 1 | ; |
| 3 |
| (A + C)'s 1 hour's work = | 1 | . |
| 2 |
| (A + B + C)'s 1 hour's work = |  |
1 | + | 1 |  |
= | 7 | . |
| 4 | 3 | 12 |
| B's 1 hour's work = | |
7 | - | 1 | |
= | 1 | . |
| 12 | 2 | 12 |
B alone will take 12 hours to do the work.
Discussion:
97 comments Page 3 of 10.
Don said:
5 years ago
How 7/12 - 1/2 = 1/12? Explain this.
Lazy Balu said:
6 years ago
A+(B+C)-(C+A) = 1/4+1/3-1/2.
A+B+C-C-A = (3+4-6)/12.
Therefore B = 1/12.
So B can do in 12 days.
A+B+C-C-A = (3+4-6)/12.
Therefore B = 1/12.
So B can do in 12 days.
Soumyaranjan said:
6 years ago
A = 4hrs.
B+C = 3hrs.
A+C = 2hrs.
Work=LCM(4, 3,2) = 12.
The efficiency of A = 12/4 = 3.
The efficiency of BC = 12/3 = 4.
The efficiency of AC = 12/2 = 6.
The efficiency of C = efficiency of (AC-A)
= 6-3 = 3
The efficiency of B = efficiency of (BC-C)
= 4-3 = 1
T = W/E
= 12/1 = 12.
So, B alone will take 12hrs for do it.
B+C = 3hrs.
A+C = 2hrs.
Work=LCM(4, 3,2) = 12.
The efficiency of A = 12/4 = 3.
The efficiency of BC = 12/3 = 4.
The efficiency of AC = 12/2 = 6.
The efficiency of C = efficiency of (AC-A)
= 6-3 = 3
The efficiency of B = efficiency of (BC-C)
= 4-3 = 1
T = W/E
= 12/1 = 12.
So, B alone will take 12hrs for do it.
(3)
Shreya said:
6 years ago
A takes 4hrs.
B+C takes 3 hrs.
A+C takes 2 hrs.
A=a.
B+C=b,
A+C=c
LCM of 4,3,2=12.
a+b+c=12units(total work done).
a=A.
So A takes 4h for 12u.
In 1 hr it does 3u.
b=B+C,
B+C take 3h for 12u.
In 1h does 4u,
c=A+C.
A+C take 2h for 12u,
in 1hr A+C do 6u.
A does 3u/h.
replacing in A+C.
3+C=6.
C=3,
C does 3u/h.
Replacing C in B+C
In 1 hr;
B+3=4.
B=1.
B does 1u/h.
1 unit of work in 1hr.
12 unit of work in 12 hrs.
B+C takes 3 hrs.
A+C takes 2 hrs.
A=a.
B+C=b,
A+C=c
LCM of 4,3,2=12.
a+b+c=12units(total work done).
a=A.
So A takes 4h for 12u.
In 1 hr it does 3u.
b=B+C,
B+C take 3h for 12u.
In 1h does 4u,
c=A+C.
A+C take 2h for 12u,
in 1hr A+C do 6u.
A does 3u/h.
replacing in A+C.
3+C=6.
C=3,
C does 3u/h.
Replacing C in B+C
In 1 hr;
B+3=4.
B=1.
B does 1u/h.
1 unit of work in 1hr.
12 unit of work in 12 hrs.
Sohail said:
7 years ago
How, (7/12 - 1/2) = 1/12?
Explain this step please.
Explain this step please.
Dev said:
7 years ago
LET THE B CAN DO WORK IN X DAYS.
PART OF THE WORK IS DONE BY B+C = 1/3.
PART OF THE WORK IS DONE BY A+C = 1/2.
Now (B+C) - (A+C) = 1/3-1/2.
B-A = 1/3-1/2.
1/x-1/4 = 1/3-1/2.
1/x = 1/12 part of work.
So Work will be completed by B alone in 12 days.
PART OF THE WORK IS DONE BY B+C = 1/3.
PART OF THE WORK IS DONE BY A+C = 1/2.
Now (B+C) - (A+C) = 1/3-1/2.
B-A = 1/3-1/2.
1/x-1/4 = 1/3-1/2.
1/x = 1/12 part of work.
So Work will be completed by B alone in 12 days.
Akshay Sen said:
7 years ago
Work done by A in one hr = 1/4.
As A+C = 2hr.
so, C's working for 1 hr will be = 1/2 -1/4 (A's working).
C's working for 1hr = 1/4.
Now As B+C = 3hrs.
so, we can find the working of B in 1 hr.
therefore working of B in 1 hr = 1/3 - 1/4.
B's = 1/12.
Hence 12hrs taken by B.
As A+C = 2hr.
so, C's working for 1 hr will be = 1/2 -1/4 (A's working).
C's working for 1hr = 1/4.
Now As B+C = 3hrs.
so, we can find the working of B in 1 hr.
therefore working of B in 1 hr = 1/3 - 1/4.
B's = 1/12.
Hence 12hrs taken by B.
Tejs said:
7 years ago
Thanks for your answer @Bits.
Sukumar said:
7 years ago
Well said @Hindu.
Akshay Ladwa said:
7 years ago
A=B+C(given) ----> (1)
one day work of A+B=1/10 --> (2)
one day work of C=1/50 ---> (3).
So for total (A+B+C)'s 1 day work, we can assume from 1--> C=A-B=1/50----> (4)
So adding equation 2 and 4 we get A=3/50.
Substituting above A in equation 2 we get B=1/25.
Hence 25 days because(If A's 1 day's work =1/n then A can finish the work in n days.)).
one day work of A+B=1/10 --> (2)
one day work of C=1/50 ---> (3).
So for total (A+B+C)'s 1 day work, we can assume from 1--> C=A-B=1/50----> (4)
So adding equation 2 and 4 we get A=3/50.
Substituting above A in equation 2 we get B=1/25.
Hence 25 days because(If A's 1 day's work =1/n then A can finish the work in n days.)).
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