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 5 of 10.
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.
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.
Sohail said:
7 years ago
How, (7/12 - 1/2) = 1/12?
Explain this step please.
Explain this step please.
Akhil said:
10 years ago
A = 4 (ie A completes the work in 4 hours)
B + C in 3.
A + C in 2.
By taking LCM 4, 3, 2 = Total work or LCM is 12hrs work.
A 1-hour work is 3/ 3*4 = 12 (ie takes 4 hours to complete total work 12 hours already given in question follow same with B + C and A + C).
B + C 1 hour work is 4/4*3 = 12.
A + C 1 hour work is 6/6*2 = 12.
A = 3
B + C = 4
A + C = 6
3A + 3C
1B + 3C
A = 3
B = 1
C = 3
So, B takes 1hr x12 = 12 hour to complete the work.
B + C in 3.
A + C in 2.
By taking LCM 4, 3, 2 = Total work or LCM is 12hrs work.
A 1-hour work is 3/ 3*4 = 12 (ie takes 4 hours to complete total work 12 hours already given in question follow same with B + C and A + C).
B + C 1 hour work is 4/4*3 = 12.
A + C 1 hour work is 6/6*2 = 12.
A = 3
B + C = 4
A + C = 6
3A + 3C
1B + 3C
A = 3
B = 1
C = 3
So, B takes 1hr x12 = 12 hour to complete the work.
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.
Don said:
5 years ago
How 7/12 - 1/2 = 1/12? Explain this.
Abhimanyu said:
5 years ago
A = 4 B + C = 3 A + C = 2.
(B+C) - (A+C) + A = B(Making equation such that we will get value of B)
1/3 -1/2 + 1/4 = B.
B = 4 - 6 + 3/12(By taking kam) = 1/12.
B = 12.
(B+C) - (A+C) + A = B(Making equation such that we will get value of B)
1/3 -1/2 + 1/4 = B.
B = 4 - 6 + 3/12(By taking kam) = 1/12.
B = 12.
Pallabi Sethi said:
4 years ago
A 1 hours work=1/4 ----> (i)
B+C 1 hors work=1/3 ----> (ii)
A+C 1 hour work=1/2 ----> (iii).
By subtracting from (iii) to (ii) we get A-B = 1/6.
Now in place of A put the value of A = 1/4.
1/4-B = 1/6,
1/4-1/6 = B.
1/12 IS B'S 1 Hour's work.
B will take 12 hours.
B+C 1 hors work=1/3 ----> (ii)
A+C 1 hour work=1/2 ----> (iii).
By subtracting from (iii) to (ii) we get A-B = 1/6.
Now in place of A put the value of A = 1/4.
1/4-B = 1/6,
1/4-1/6 = B.
1/12 IS B'S 1 Hour's work.
B will take 12 hours.
Kavit vaishnav said:
1 month ago
A takes 4 hours, 1 hour work = 25%.
For A+C = 2 hours =100% work.
A's part = 50%(for 2 hours),
Remaining part done by C 50% in time 2 hours. So C also does 25% in 1 hour.
Now B+C = 3 Hours = 100% work.
C's part = 3*25% = 75% in 3 hours.
B's part = remaining work = 25% in 3 hours.
So, B' s efficiency = 100% in 12 hours.
For A+C = 2 hours =100% work.
A's part = 50%(for 2 hours),
Remaining part done by C 50% in time 2 hours. So C also does 25% in 1 hour.
Now B+C = 3 Hours = 100% work.
C's part = 3*25% = 75% in 3 hours.
B's part = remaining work = 25% in 3 hours.
So, B' s efficiency = 100% in 12 hours.
Arjun said:
1 decade ago
Total =4
b&c =3...1
a&c= 2...2
we have to find c so 1 c is 3 therefore 3*4=12
Hey guys let me know if i am correct.
b&c =3...1
a&c= 2...2
we have to find c so 1 c is 3 therefore 3*4=12
Hey guys let me know if i am correct.
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