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:
100 comments Page 8 of 10.
Hindu said:
2 decades ago
Take the given data as 2 equations as follows
A=1\4 ,B+C=1\3--eq1 and A+C=1\2---eq2
put A=1\4 in eq2
1\4+C=1\2
C=1\2-1\4 we get
C=1\4
put C=1\4 in eq1
B+1\4=1\3
B=1\3-1\4 we get
B=1\12
Therefore B alone take 12hours to do a work
A=1\4 ,B+C=1\3--eq1 and A+C=1\2---eq2
put A=1\4 in eq2
1\4+C=1\2
C=1\2-1\4 we get
C=1\4
put C=1\4 in eq1
B+1\4=1\3
B=1\3-1\4 we get
B=1\12
Therefore B alone take 12hours to do a work
Ashish said:
2 decades ago
Good question. Reasoning is difficult for this one.
Nagendramurthy said:
2 decades ago
Hi friends,
(A+C-A)=C
(1/2-1/4)=1/4
so C's 1 hour work will be 1/4.
Similarly
(B+C-C)=B
(1/3-1/4)=1/12
Therefore B's 1 hour work is 1/12.
(A+C-A)=C
(1/2-1/4)=1/4
so C's 1 hour work will be 1/4.
Similarly
(B+C-C)=B
(1/3-1/4)=1/12
Therefore B's 1 hour work is 1/12.
Nagarjun said:
2 decades ago
A's 1 hour work is 1/4
(A+C)'s 1 hour work is 1/2
(B+C)'s 1 hour work is 1/3
so, A+C=1/2 ->X and B+C=1/3 ->Y
subtract X-Y
we will get A-B=1/6
now, substitute A's value in d equation u vl get B's value as 1/12.
which is 1 day,s work of B...
hence B alone require 12 days...
I HOPE IT VL B HELPFULL...
(A+C)'s 1 hour work is 1/2
(B+C)'s 1 hour work is 1/3
so, A+C=1/2 ->X and B+C=1/3 ->Y
subtract X-Y
we will get A-B=1/6
now, substitute A's value in d equation u vl get B's value as 1/12.
which is 1 day,s work of B...
hence B alone require 12 days...
I HOPE IT VL B HELPFULL...
Varseyny said:
2 decades ago
A=1/4 (given)
(B+C)=1/3 (given)
(A+B+C)=(1/4+1/3) then take L.C.M
3+4/12=7/12
FIND FOR B
A+B+C=7/12
B=7/12-(A+C) given(A+C=1/2)
B=7/12-(1/2)=1/12
ANS:12
(B+C)=1/3 (given)
(A+B+C)=(1/4+1/3) then take L.C.M
3+4/12=7/12
FIND FOR B
A+B+C=7/12
B=7/12-(A+C) given(A+C=1/2)
B=7/12-(1/2)=1/12
ANS:12
Saleem said:
1 decade ago
Hi.
A = 1/4....(1).
B+C = 1/3....(2).
A+C = 1/2....(3).
Now solve equation (1) & (3).
1/4+C = 1/2.
C = 1/4....(4).
Put C value in equation (2).
B+1/4 = 1/3.
B = 1/3-1/4.
B = 1/12 that's the answer.
A = 1/4....(1).
B+C = 1/3....(2).
A+C = 1/2....(3).
Now solve equation (1) & (3).
1/4+C = 1/2.
C = 1/4....(4).
Put C value in equation (2).
B+1/4 = 1/3.
B = 1/3-1/4.
B = 1/12 that's the answer.
Akshay Jaywant said:
1 decade 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:
1 decade 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.
Haripriya said:
1 decade 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.
Sagar raut said:
1 decade 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.
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