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 7 of 10.
Avinash said:
1 decade ago
A's 1day wrk------>1/4
B+C's 1day wrk---->1/3
A+C's 1day wrk---->1/2
(A+C)-A=1/2-1/4=1/2 ie.. c=1/4
so B+1/4=1/3--->b=1/12
B+C's 1day wrk---->1/3
A+C's 1day wrk---->1/2
(A+C)-A=1/2-1/4=1/2 ie.. c=1/4
so B+1/4=1/3--->b=1/12
Vinod Anand said:
1 decade ago
If A = 4 -(1)
B+C = 3 -(2)
A+C = 2 -(3)
From Eq.(1) and (2)
4C = 2-1, C = 4 (4' is coming from LCM and 4/4 = 1 and 4/2 = 2,
So 2-1 = 1 and 4/1 = 4).
Put the value of C in eq.(2).
12 B = 4-3.
Than B = 12 hours, Option -C.
B+C = 3 -(2)
A+C = 2 -(3)
From Eq.(1) and (2)
4C = 2-1, C = 4 (4' is coming from LCM and 4/4 = 1 and 4/2 = 2,
So 2-1 = 1 and 4/1 = 4).
Put the value of C in eq.(2).
12 B = 4-3.
Than B = 12 hours, Option -C.
Ankur said:
1 decade ago
B+C=1/3
A+C=1/2
A+C-(B+C)=1/2-1/3
A-B=1/6
B=A-1/6
B=1/4-1/6
B=1/12
ie 12 is the ans
A+C=1/2
A+C-(B+C)=1/2-1/3
A-B=1/6
B=A-1/6
B=1/4-1/6
B=1/12
ie 12 is the ans
Asha said:
1 decade ago
There is one more method for this question, a shortcut formula. A theorem says if A and B together can do a piece of work in x days, and A alone can do it in y days, then B alone can do the work in xy/y-x days.
Therefore for AC pair C's work hrs = 4*2/4-2= 4 hrs
now for BC pair B's work hrs = 4*3/4-3 = 12 hrs :)
Therefore for AC pair C's work hrs = 4*2/4-2= 4 hrs
now for BC pair B's work hrs = 4*3/4-3 = 12 hrs :)
Piyus said:
1 decade ago
(b+c)of 1 hour-(a+c) of 1 hour = 1/3-1/2
=> b(1hr)-a(1hr)=(-1/6)
=> b(1hr)=1/4-1/6
=>b's 1hr work= 1/12
=>b ll take 12 hr to complete the work alone
=> b(1hr)-a(1hr)=(-1/6)
=> b(1hr)=1/4-1/6
=>b's 1hr work= 1/12
=>b ll take 12 hr to complete the work alone
Pavan@9966606261 said:
1 decade ago
Hi friends
b+c=1/3;
a+c=1/2;
a=1/4;
c=1/2-1/4=1/4;
b=1/3-1/4=1/12;
time taken for B alone to complete is 12 hours
b+c=1/3;
a+c=1/2;
a=1/4;
c=1/2-1/4=1/4;
b=1/3-1/4=1/12;
time taken for B alone to complete is 12 hours
Jayanth babu said:
1 decade ago
Hi friends, in above problem
A=1/4----->(1)
B+C=1/3----->(2)
A+C=1/2------>(3)
now solving (2)
B+C=1/3
c=B-1/3--------->(4)
substitute (1) and (4) in (3)
then..
(1/4)+B-(1/3)=1/2
by solving this equation
B=1/12
Thus, B alone take 12hrs.
A=1/4----->(1)
B+C=1/3----->(2)
A+C=1/2------>(3)
now solving (2)
B+C=1/3
c=B-1/3--------->(4)
substitute (1) and (4) in (3)
then..
(1/4)+B-(1/3)=1/2
by solving this equation
B=1/12
Thus, B alone take 12hrs.
HARRY said:
1 decade ago
C=1/2-1/4=>1/4(C'S 1 DAY WORK)
B=1/3-1/4=>1/12(B'S 1 DAY WORK)
SO 12 DAYS TO COMPLETE THE WORK
B=1/3-1/4=>1/12(B'S 1 DAY WORK)
SO 12 DAYS TO COMPLETE THE WORK
Hindu said:
1 decade 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:
1 decade ago
Good question. Reasoning is difficult for this one.
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