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:
98 comments Page 5 of 10.
Sandeep choudhary said:
9 years ago
A = 4.
B + C = 3.
A + C = 2.
Take LCM = 12.
ONE DAY WORK OF A = 12/4 = 3.
Similarly, B + C = 12/3 = 4------>1.
A+C = 12/2 = 6------> 2.
TOTAL ONE DAY WORK = 13.
PUT VALUE OF A in Eqn 2 and got the value of B then put in eqn 1 and got value of c=12.
B + C = 3.
A + C = 2.
Take LCM = 12.
ONE DAY WORK OF A = 12/4 = 3.
Similarly, B + C = 12/3 = 4------>1.
A+C = 12/2 = 6------> 2.
TOTAL ONE DAY WORK = 13.
PUT VALUE OF A in Eqn 2 and got the value of B then put in eqn 1 and got value of c=12.
Reshma said:
9 years ago
A = 1/4.
B + C = 1/3.
A + C = 1/2.
Subtract the above 2 equations we get,
B - A = 1/3 - 1/2,
B - A = -1/6,
B = -1/6 + 1/4,
B = 1/12,
So, B takes 12 hours to complete the work.
B + C = 1/3.
A + C = 1/2.
Subtract the above 2 equations we get,
B - A = 1/3 - 1/2,
B - A = -1/6,
B = -1/6 + 1/4,
B = 1/12,
So, B takes 12 hours to complete the work.
Chiru said:
9 years ago
Thank you everyone for the clear explanation.
Anjum said:
9 years ago
Thank you everyone for the clear explanation.
Anil said:
9 years ago
By solving this three equation, we will get the answer.
1/A = 1/4.
1/B + 1/C = 1/3.
1/A + 1/C = 1/2.
1/A = 1/4.
1/B + 1/C = 1/3.
1/A + 1/C = 1/2.
Prajwal said:
9 years ago
A = 1/4.
B + C= 1/3.
A + C= 1/2.
B = ?
C = 1/2 - A.
C = 1/2 - 1/4 = 1/4.
B = 1/3 - C.
B = 1/3 - 1/4.
B = 1/12.
B takes 12 hrs.
B + C= 1/3.
A + C= 1/2.
B = ?
C = 1/2 - A.
C = 1/2 - 1/4 = 1/4.
B = 1/3 - C.
B = 1/3 - 1/4.
B = 1/12.
B takes 12 hrs.
Swaathi said:
10 years ago
A = 1/4,
(B + C ) = 1/3,
(A + C ) = 1/2,
Subtract ( A + C ) and A,
We get C = 1/4 and then subtract (B + C ) and C,
We get B = 1/12,
Therefore 12 hours.
(B + C ) = 1/3,
(A + C ) = 1/2,
Subtract ( A + C ) and A,
We get C = 1/4 and then subtract (B + C ) and C,
We get B = 1/12,
Therefore 12 hours.
Ashim said:
10 years ago
4A = 3 (B + C) = 2 (A + C).
4A = 2A + 2C, A = C.
3B + 3C = 2A + 2C.
3B = C.
Or 3B = A.
If A takes 4 hours to complete the work than B takes 12 hours.
4A = 2A + 2C, A = C.
3B + 3C = 2A + 2C.
3B = C.
Or 3B = A.
If A takes 4 hours to complete the work than B takes 12 hours.
Akshay Jaywant said:
10 years ago
Thanks to all of my friends giving the wonderful methods.
It's very simple.
A + (B + C) - (A + C) = B.
1/4 + 1/3 - 1/2 = 1/12.
Therefore, 12 hrs.
It's very simple.
A + (B + C) - (A + C) = B.
1/4 + 1/3 - 1/2 = 1/12.
Therefore, 12 hrs.
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.
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