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 







So, A and C together will do the work in 8 days.
Discussion:
53 comments Page 1 of 6.
Kabir NSEC said:
1 year 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 = 42 = 2
Eff. of C= 43 = 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 = 42 = 2
Eff. of C= 43 = 1.
So, eff of AC = 2 + 1 = 3
time to finish for AC = 24/3 = 8.
(21)
Pratiksha said:
1 year 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.
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.
(31)
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:
3 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)=42 =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)=42 =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.
(6)
SIVA said:
4 years ago
Good explanation. Thanks all.
(1)
Pandeswari Durai Pandi said:
4 years ago
@Nanthu.
Thank you for using LCM method it makes me to understand it easily.
Thank you for using LCM method it makes me to understand it easily.
Jigme Wangchuk said:
4 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 42= 2 units.
C works 43= 1 units.
Total work done by A+C = 2+1= 3 units.
Therefore, 24/3= 8.
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 42= 2 units.
C works 43= 1 units.
Total work done by A+C = 2+1= 3 units.
Therefore, 24/3= 8.
(12)
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.
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.
(16)
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, (832/24).
85/24>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, (832/24).
85/24>3/24.
A+C = 1/8 days.
so the answer is 8 days.
(5)
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