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 1 of 6.
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)
Gaurab.bc said:
4 years ago
A+B = 8
B+C=12
A+B+C=6.
Total work LCM=24 unit work for each group to do in 1 day = 24/8=3, 24/12=2 24/6 =4 (3,2,4)
So, A alone efficiency = (A+B+C)-(B+C)=4-2 =2 so work done by in A=24/2 =12 day simiarly by B = 24/1 = 24 days.
Finally, LCM for A and B= 24 , unit work for each = 2 and 1.
So total efficency = 1+2 =3 and work done by A+B = 24/3 = 8 DAYS.
B+C=12
A+B+C=6.
Total work LCM=24 unit work for each group to do in 1 day = 24/8=3, 24/12=2 24/6 =4 (3,2,4)
So, A alone efficiency = (A+B+C)-(B+C)=4-2 =2 so work done by in A=24/2 =12 day simiarly by B = 24/1 = 24 days.
Finally, LCM for A and B= 24 , unit work for each = 2 and 1.
So total efficency = 1+2 =3 and work done by A+B = 24/3 = 8 DAYS.
(7)
Kesavan said:
5 years ago
Given question,
A + B = 1/8 days.
B + C = 1/12 days.
A + B + C = 1/6 days.
We want C+A,
(A+B) + (B+C) + (A+C) =2 (A+B+C)------->1.
Now substitute all the values in Eqn( 1).
1/8 + 1/12 + (A+C) = 2 (1/6),
(A+C) = 1/3 - 1/8 - 1/12.
Now I Take lcm, (8-3-2/24).
8-5/24----->3/24.
A+C = 1/8 days.
so the answer is 8 days.
A + B = 1/8 days.
B + C = 1/12 days.
A + B + C = 1/6 days.
We want C+A,
(A+B) + (B+C) + (A+C) =2 (A+B+C)------->1.
Now substitute all the values in Eqn( 1).
1/8 + 1/12 + (A+C) = 2 (1/6),
(A+C) = 1/3 - 1/8 - 1/12.
Now I Take lcm, (8-3-2/24).
8-5/24----->3/24.
A+C = 1/8 days.
so the answer is 8 days.
(8)
Y. Balaji said:
1 decade ago
@ Jeev.
Don't worry and don't confuse. Just think.
A+B+C = 1/6 => equation 1.
A+B = 1/8 => equation 2.
B+C = 1/12 => equation 3.
From equation 1&3 (1-3).
A = (1/6) - (1/12) = (1/12) => 4.
From equation 1&2 (1-2).
C = (1/6) - (1/8) = (1/24) => 5.
Now A+C = (1/12) + (1/24) = 1/8.
= 8 days.
Don't worry and don't confuse. Just think.
A+B+C = 1/6 => equation 1.
A+B = 1/8 => equation 2.
B+C = 1/12 => equation 3.
From equation 1&3 (1-3).
A = (1/6) - (1/12) = (1/12) => 4.
From equation 1&2 (1-2).
C = (1/6) - (1/8) = (1/24) => 5.
Now A+C = (1/12) + (1/24) = 1/8.
= 8 days.
Santosh said:
7 years ago
A+B ....8 DAY- 3unit. L.C.M-24 UNIT
B+C......12 DAY - 2 unit.
A+B+C......6 DAY -(24/6)...4 unit .
Then,
A+B+C=4. A+B=3....(3+C=4 =C=1)
C=1.
B+C=2 UNIT .....C=1.
B=1.
A+B=3.
B=1.
A=2 .
A and c's work.
A+c=2+1=3 unit per day,
Total work =24 unit,
A+c=24/3=8 day.
B+C......12 DAY - 2 unit.
A+B+C......6 DAY -(24/6)...4 unit .
Then,
A+B+C=4. A+B=3....(3+C=4 =C=1)
C=1.
B+C=2 UNIT .....C=1.
B=1.
A+B=3.
B=1.
A=2 .
A and c's work.
A+c=2+1=3 unit per day,
Total work =24 unit,
A+c=24/3=8 day.
Sonam said:
10 years ago
For easy understanding:.
A+B= 1/8 --> 1.
B+C= 1/12 --> 2.
A+B+C= 1/6 --> 3.
We need to find A+C.
Substitute equation 1 in equation 3 you will get C= 1/24.
Substitute equation 2 in equation 3 you will get A= 1/12.
Now add A+C --> 1/12 + 1/24 = 1/8.
= 8 days.
Hope this helps you.
A+B= 1/8 --> 1.
B+C= 1/12 --> 2.
A+B+C= 1/6 --> 3.
We need to find A+C.
Substitute equation 1 in equation 3 you will get C= 1/24.
Substitute equation 2 in equation 3 you will get A= 1/12.
Now add A+C --> 1/12 + 1/24 = 1/8.
= 8 days.
Hope this helps you.
(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.
Kabir NSEC said:
2 years ago
@All.
Total work: lcm of 8, 12 and 6. (For easy divisibility)= 24,
Eff = total work/days needed to do the job.
Efficiencies:
AB:24/8 = 3
BC:24/12 = 2
ABC:24/6 = 4.
Eff. of A = ABCeff - BCeff = 4-2 = 2
Eff. of C= 4-3 = 1.
So, eff of AC = 2 + 1 = 3
time to finish for AC = 24/3 = 8.
Total work: lcm of 8, 12 and 6. (For easy divisibility)= 24,
Eff = total work/days needed to do the job.
Efficiencies:
AB:24/8 = 3
BC:24/12 = 2
ABC:24/6 = 4.
Eff. of A = ABCeff - BCeff = 4-2 = 2
Eff. of C= 4-3 = 1.
So, eff of AC = 2 + 1 = 3
time to finish for AC = 24/3 = 8.
(33)
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.
Vishal sinha said:
6 years ago
It can be done in a much simpler way.
(A+B)'s 1-day work = 1/8.
(B+C)'s 1-day work = 1/12.
(A+B)+(B+C)'s 1 day work= 1/8+1/12.
B+(A+B+C)=5/24,
B=5/24-1/6,
B=1/24.
So, A+B+C=1/6,
Putting the value of B.
(A+C)'s 1 day work = 1/6 - 1/24 = 1/8.
Time taken = 8 days.
(A+B)'s 1-day work = 1/8.
(B+C)'s 1-day work = 1/12.
(A+B)+(B+C)'s 1 day work= 1/8+1/12.
B+(A+B+C)=5/24,
B=5/24-1/6,
B=1/24.
So, A+B+C=1/6,
Putting the value of B.
(A+C)'s 1 day work = 1/6 - 1/24 = 1/8.
Time taken = 8 days.
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