# 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 :
4 days
6 days
8 days
12 days
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
 = 2 x 1 - 1 + 1 6 8 12
 = 1 - 5 3 24
 = 3 24
 = 1 . 8

So, A and C together will do the work in 8 days.

Discussion:
53 comments Page 1 of 6.

Kabir NSEC said:   8 months 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.
(12)

Pratiksha said:   10 months ago
A + B = 1/8.
B + C = 1/12.
A + B + C = 1/6.
C = A + B + C - A + B.
C = 1/6 - 1/8 = 1/24,
A = A + B + B - B + C,
A = 1/6 - 1/12 = 1/12
A + C = 1/12 + 1/24,
A + C = 1/8,
A + C = 8days.
(16)

Tanveer sayyed said:   2 years ago
5/24 how? anyone explain.
(1)

Ivan said:   2 years ago
Thanks for explaining @Parveen Verma.
(1)

Gaurab.bc said:   2 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.
(4)

SIVA said:   3 years ago
Good explanation. Thanks all.
(1)

Pandeswari Durai Pandi said:   3 years ago
@Nanthu.

Thank you for using LCM method it makes me to understand it easily.

Jigme Wangchuk said:   3 years ago
Lcm of 8 and 12 =24.
A + B works 24/3 = 3 units.
B + C works 24/12 = 2 units.
A + B + C works 24/6 = 4 units.
Now, A works 4-2= 2 units.
C works 4-3= 1 units.

Total work done by A+C = 2+1= 3 units.
Therefore, 24/3= 8.
(7)

Pranav Ambore said:   4 years ago
A+B+C=1/6 ---------> (1)
A+B=1/8 --------------> (2)
B+C=1/12-------------> (3)

By using(1) & (2).
1/8+c = 1/6.
c = 1/24.

By using(1) & (3).
A+1/12 = 1/6.
A = 1/12.
A + C = 1/12+ 1/24 = 1/8.
8 days.
(14)

Kesavan said:   4 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.
(1)