Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 26)
26.
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
Answer: Option
Explanation:
| (A + B + C)'s 1 day's work = | 1 | ; |
| 6 |
| (A + B)'s 1 day's work = | 1 | ; |
| 8 |
| (B + C)'s 1 day's work = | 1 | . |
| 12 |
 (A + C)'s 1 day's work |
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So, A and C together will do the work in 8 days.
Discussion:
53 comments Page 2 of 6.
Basu said:
1 decade ago
How its come on 1/6-1/2=1/12
1/6-1/8= 1/24
1/12+1/24= 1/8
1/6-1/8= 1/24
1/12+1/24= 1/8
Nice dreamer said:
1 decade ago
Why 2 is multiplied with 1/6 ? please explain any one.
Nik said:
1 decade ago
1 day's work of(A+B)=1/8
1 day's work of (B+C)=1/12
lets take 1 day's work of (A+C)=1/x
adding the above we get 2(A+B+C)=1/8+1/12+1/X
dr4 2(1/6)=(1/8)+(1/12)+(1/x)
1/x=(2/6)-(1/8)-(1/12)
1/x=1/8
1 day's work of (B+C)=1/12
lets take 1 day's work of (A+C)=1/x
adding the above we get 2(A+B+C)=1/8+1/12+1/X
dr4 2(1/6)=(1/8)+(1/12)+(1/x)
1/x=(2/6)-(1/8)-(1/12)
1/x=1/8
Dhanshree said:
1 decade ago
(A+B) work is = 1/8.
(B+C)work is = 1/12.
(A+B+C)work is = 1/6.
Only A's work = 1/6-1/12
= 1/12.
Only C's work=1/6-1/8
= 1/24.
Hence (A+C)'s complete work is = (1/12+1/24)
= 1/8.
(A+C)'s complete work in 8 day.
(B+C)work is = 1/12.
(A+B+C)work is = 1/6.
Only A's work = 1/6-1/12
= 1/12.
Only C's work=1/6-1/8
= 1/24.
Hence (A+C)'s complete work is = (1/12+1/24)
= 1/8.
(A+C)'s complete work in 8 day.
Monu said:
1 decade ago
Why can't we simply subtract A+B's 1 day work from B+C's 1 day work to get A+C's 1 day work?
Sk.Gopinath said:
1 decade ago
A+B+C = 1/6;
A+B = 1/8;
B+C = 1/12;
C's 1day work is =>1/6 - 1/8
=>1/24.
A's 1day work is =>1/6 - 1/12
=>1/8.
A+C 's 1day's work =>1/24 + 1/12.
= 1/8 = 8 days.
A+B = 1/8;
B+C = 1/12;
C's 1day work is =>1/6 - 1/8
=>1/24.
A's 1day work is =>1/6 - 1/12
=>1/8.
A+C 's 1day's work =>1/24 + 1/12.
= 1/8 = 8 days.
Iqbal sofi said:
1 decade ago
This can be easily solved as:
Given that,
A+B=8 => A+B=1/8;..........(1).
B+C=12 => B+C=1/12;...........(2).
&
A+B+C=6 => A+B+C=1/6;...........(3).
solving eq (3).
A+(B+C) = 1/6.
A+(1/12) = 1/6.
A = 1/6-1/12.
A = 1/12.
Substitute A in eq (1),
A+B = 1/8.
(1/12)+B = 1/8.
B = 1/8-1/12.
B = 1/24.
now substitute B in eq (2)
B+c=1/12
(1/24)+c=12
c=1/12-1/24
c=1/24
Question is A+c=?
(1/12)+(1/24).
1/8.
Therefore A and C can do the work in 8 days.
Given that,
A+B=8 => A+B=1/8;..........(1).
B+C=12 => B+C=1/12;...........(2).
&
A+B+C=6 => A+B+C=1/6;...........(3).
solving eq (3).
A+(B+C) = 1/6.
A+(1/12) = 1/6.
A = 1/6-1/12.
A = 1/12.
Substitute A in eq (1),
A+B = 1/8.
(1/12)+B = 1/8.
B = 1/8-1/12.
B = 1/24.
now substitute B in eq (2)
B+c=1/12
(1/24)+c=12
c=1/12-1/24
c=1/24
Question is A+c=?
(1/12)+(1/24).
1/8.
Therefore A and C can do the work in 8 days.
(2)
Husam said:
1 decade ago
One day's work for (A+B) is 1/8.
One day's work for (B+C) is 1/12.
One day's work for (A+C) is 1/X.
So,
(A+B)+(B+C)+(A+C) = 1/8+1/12+1/x.
2(A+B+C) = 1/8+1/12+1/x.
2*1/6 = 1/8+1/12+1/x.
1/x = 2*1/6-(1/8+1/12).
x = 1/8.
So,
One day's work for (A+C) = 1/8.
A and C finish work in 8 days.
One day's work for (B+C) is 1/12.
One day's work for (A+C) is 1/X.
So,
(A+B)+(B+C)+(A+C) = 1/8+1/12+1/x.
2(A+B+C) = 1/8+1/12+1/x.
2*1/6 = 1/8+1/12+1/x.
1/x = 2*1/6-(1/8+1/12).
x = 1/8.
So,
One day's work for (A+C) = 1/8.
A and C finish work in 8 days.
Nisha said:
1 decade ago
Why 2 is multiplied with 1/6.
To find out (A+C)'s work the equation is 2(A+B+C)-((A+B)+(B+C)).
On solving this equation,
A+B+C = 1/6;
A+B = 1/8;
B+C = 1/12;
(A+C)= 2(1/6)-(1/8+1/12),
= 1/8.
To find out (A+C)'s work the equation is 2(A+B+C)-((A+B)+(B+C)).
On solving this equation,
A+B+C = 1/6;
A+B = 1/8;
B+C = 1/12;
(A+C)= 2(1/6)-(1/8+1/12),
= 1/8.
Hussain said:
1 decade ago
Hey guys please say me.
How 1/12+1/24 = 1/8.
I did not understand the logic the lcm of these two numbers is 24.
How 1/12+1/24 = 1/8.
I did not understand the logic the lcm of these two numbers is 24.
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