Aptitude - Time and Work - Discussion

@Ajay.

How to find efficiency ratio?

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.

Time ratio of A,B,C=6:3:2.
Efficiency ratio=1:2:3.

It takes 2 days for all of them to complete the work. So, Total work=(1+2+3)*2=12.

Time taken by B=12/2 = 6days.
Time taken by A=12/1 = 12days.
Time taken by C=12/3 = 4days.

@Manish, @Kiran.

Thanks for explaining the solution.

One day work of a,b&c=1/2
let a's one-day work=x , then b's one day work 2x & c work 3x
x+2x+3x=1/2
6x=1/2
x=1/12
b's one day work=2*1/12
=1/6

Therefore total work in 6 days.

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.

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).

a+2a+3a = 2days.
6a = 2days,
a = 1/3(this is total),
3*2 = 6.

@Ravi.

Where you get 12 unit work in 1 days and how please explain it?

Yes, right @Ravi.

Your method of explanation is clear, Thanks @Subhas.