Aptitude - Time and Work - Discussion

Best Solution,

Let A take x days to complete the work, Therefore in one day he completes 1/x of the work
Thus B will complete the work in x/2 days, Therefore in one day B will complete twice of A's work, i.e 2*(1/x)................(i)

Similarly in one day C will complete thrice of A's work, i.e 3*(1/x)

Together they take 2 days to complete the work, Therefore in one day they complete 1/2 or 50% of the work,.

Thus (work done by A + work done by B + work done by C) in one day = 1/2 or 50%
1/x + 2/x + 3/x = 1/2,
(1+2+3)/x = 1/2,
6/x = 1/2,
x=12, i.e The days required by A to complete the work.
Therefore B will take = x/2 = 12/2 = 6 days......................from eq.(i).

Simple Method. But I explained Elaborate.

A is twice time as B => A=2B
A is thrice time as c => A=3C
therefore;

B =A/2
C= A/3
A= A, A=2* (A/2)
A taken as X
A, B, C X, X/2, X/3 Days Respectively;
Rule of Flip or Time to Work
1/x +2//x+3/x =1/2
6/x =1/2
x=12

Asking b Alone.
B= x/2
so 12/2
B =6 Days.

@Manish, @Kiran.

Thanks for explaining the solution.

a---12 days .
b ----6 days.
c --- 4 days.
lcm of 12,6,4 = 12.

The work done in one day by
A- 1
B-2
C-3
then total work done by B in 6 days.
6 is the answer.

A - 12.
B - 6.
C - 4.

Work as satisfied to take together 2day finished.
Efficiency A 1 B 2 C 3.
Total work 12.
Total efficiency 6.
Finished together 12 ÷ 6 = 2day satisfied
**B alone do in 12 ÷ 2 = 6 days.

once c the question pls it is mentioned a is twice of b OR thrice of c then how can we divide x,x/2,x/3. if it is mentioned as and then we can decide right?

B=2A
C=3A
A+B+C=2days
A+2A+3A=2days
so,6A=2days
A only takes (6*2)=12 days
B=2A,so B only takes (12/2)=6days

Hi Mini you are making equ. 2A=B & 3A=C, but so many people a making equ. A=2B & A=3C .

Which one s correct, but both one is getting same answer. I'm confussing in this prob. Pls any one describe it ?

A=2B=3C

A+B+C=2 ----(EQ.1)

WRITING a and c in terms of b,

A=2B, C=2B/3
IN EQ.1,

2B+B+2B/3=2

3B+2B/3=2


(9B+2B)/3=2

9B+2B=2*3

11B=6

B=6/11

that means, out of 11 days, b alone completes 6 days of work.

A takes twice much time them B i.e. 2A=B...(i)
A takes thrice much time thn C i.e. 3A=C...(ii)

It is given dat workin together they can finish in 2 days
so A+B+C=1/2
Now put B=2A AND C=3A in this equ...
A+B+C=1/2
A+2A+3A=1/2
6A=1/2
A=1/2*6=1/12
Now put the value of A in equ.(i)
.i.e B=2A
=2*1/12
=1/6
Therefore B takes 6 days to complete the work.