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:
96 comments Page 5 of 10.
TEJASHWINI said:
1 decade ago
A =1/4 then substitute in A+C = 1/2 we get 1/4+C = 1/2.
C = 1/2-1/4 = 1/4.
Substitute this value of C in B+C = 1/3 we get B+1/4 = 1/3.
B = 1/3-1/4 = 1/12.
Answer is 12 hours.
C = 1/2-1/4 = 1/4.
Substitute this value of C in B+C = 1/3 we get B+1/4 = 1/3.
B = 1/3-1/4 = 1/12.
Answer is 12 hours.
Abhin said:
10 years ago
By the way why we are reciprocating 1/12 into 12?
Ajay said:
10 years ago
For these type of questions,
Try to combine a+b+c and and evaluate each type.
Try to combine a+b+c and and evaluate each type.
Suni said:
10 years ago
A's one day work = 1/4......(1).
(B+C)'s one day work = 1/3.....(2).
(A+C) 's one day work = 1/2......(3).
i.e, B+C = 1/3......(4).
(5)-(4).
A+C= 1/2......(5).
A-B = 1/2-1/3 = 1/6.
A-B = 1/6 (since A = 1/4).
1/4-1/6 = B.
B = 1/12.
Answer: 12 hrs.
(B+C)'s one day work = 1/3.....(2).
(A+C) 's one day work = 1/2......(3).
i.e, B+C = 1/3......(4).
(5)-(4).
A+C= 1/2......(5).
A-B = 1/2-1/3 = 1/6.
A-B = 1/6 (since A = 1/4).
1/4-1/6 = B.
B = 1/12.
Answer: 12 hrs.
Saurabh said:
10 years ago
Following method focuses on avoiding fractions as much as possible, because calculating with fractions takes longer amount of time than calculating with integers.
In most problems on work-time-rate, fractions can be avoided altogether, or at least the role of fractions can be minimized.
Solution:
Assume total work = LCM (4, 3, 2) units = 12 units.
A's time = 4 hr.
==> A's rate = 12 units/4 hr = 3 units/hr.....(1).
(B+C)'s time = 3 hr.
==> B's rate + C's rate = 12 units/3 hr = 4 units/hr.....(2).
(A+C)'s time = 2 hr.
==> A's rate + C's rate = 12 units/2 hr = 6 units/hr.....(3).
From (1) and (3),
C's rate = 6-3 = 3 units/hr.....(4).
From (2) and (4),
B's rate = 4-3 = 1 unit/hr.
Hence B's time = Total work/B's rate = 12/1 = 12 hours.
Note: If you want to avoid spending time calculating the LCM, you can do so by saying that total amount of work = 4x3x2 = 24 units. Further calculations will change accordingly, but final answer will still be 12 hours.
The trick is "Don't define the total work to be simply 1 unit". Whenever the total work is defined to be 1 unit, fractions are introduced in the solution almost inevitably. Instead, we keep the total amount of work problem specific, and choose the total number of units to be the multiplication (or LCM) of suitable numbers.
While there is no guarantee that the fractions will be avoided altogether, they will at least be reduced to a large extent. In many cases, even some complicated ratios can be avoided by this method.
I will try to post as many solutions as I can using this method.
In most problems on work-time-rate, fractions can be avoided altogether, or at least the role of fractions can be minimized.
Solution:
Assume total work = LCM (4, 3, 2) units = 12 units.
A's time = 4 hr.
==> A's rate = 12 units/4 hr = 3 units/hr.....(1).
(B+C)'s time = 3 hr.
==> B's rate + C's rate = 12 units/3 hr = 4 units/hr.....(2).
(A+C)'s time = 2 hr.
==> A's rate + C's rate = 12 units/2 hr = 6 units/hr.....(3).
From (1) and (3),
C's rate = 6-3 = 3 units/hr.....(4).
From (2) and (4),
B's rate = 4-3 = 1 unit/hr.
Hence B's time = Total work/B's rate = 12/1 = 12 hours.
Note: If you want to avoid spending time calculating the LCM, you can do so by saying that total amount of work = 4x3x2 = 24 units. Further calculations will change accordingly, but final answer will still be 12 hours.
The trick is "Don't define the total work to be simply 1 unit". Whenever the total work is defined to be 1 unit, fractions are introduced in the solution almost inevitably. Instead, we keep the total amount of work problem specific, and choose the total number of units to be the multiplication (or LCM) of suitable numbers.
While there is no guarantee that the fractions will be avoided altogether, they will at least be reduced to a large extent. In many cases, even some complicated ratios can be avoided by this method.
I will try to post as many solutions as I can using this method.
NARESH PAL said:
10 years ago
(A + B) - B = B + C (A and B, C works equal).
1/10 - B = B + C.
1/2B = 1/10 - 1/50.
B = 25.
1/10 - B = B + C.
1/2B = 1/10 - 1/50.
B = 25.
Sagar raut said:
10 years ago
A's 1 day work is 1/4.
A and B 1 day work is 1\3.
So 1/(A+B)-1\A = 1\B.
1\3 - 1\4 = 1\12.
A and B 1 day work is 1\3.
So 1/(A+B)-1\A = 1\B.
1\3 - 1\4 = 1\12.
Haripriya said:
9 years ago
a = 1/4;
b+c = 1/3;
a+c = 1/2.
Therefore find the c value first:- a+c = 1/2.
1/4+c = 1/2.
c = 1/4.
Now substitute in b+c = 1/3.
b+1/4 = 1/3.
b = 1/12 hence it takes 12 hours.
b+c = 1/3;
a+c = 1/2.
Therefore find the c value first:- a+c = 1/2.
1/4+c = 1/2.
c = 1/4.
Now substitute in b+c = 1/3.
b+1/4 = 1/3.
b = 1/12 hence it takes 12 hours.
Akhil said:
9 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.
Akshay Jaywant said:
9 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.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers