Aptitude - Time and Work - Discussion

Assume total work iso no of chairs from the give no of chair made per one day as per efficiency
A : B : C = 1 : 2 : 3.
So total chairs is 6 in one day.
Total days they together : 2 days.
So, total works = 6 * 2 = 12.
B alone can take = 12/2 = 6 days.

A : B : C = 6 : 3 : 2,
11*2= 22 work,
So, B doing = (3/11) * 22 = 6 days.

A x.
B 2x.
C 3x.

A+B+B = 1/2,
X+2x+3x = 1/2.
6x=1/2.
X=1/12.

So, be alone =2x = 2 * 1/12 = 1/6 = 6days.

To simple method is:
A = 2B or A=3B
(A+B)'s 1day work = 1/2=(2B+B)'s 1day work
1/2 = 3B's 1-day work
ie, B's 1 day work = 1/6
So, B's whole work done is in 6 days.

Simply, it is solved by;

A=2B ; A=3C.
A/2=B ; A/3=C ---> time,
2/A=B; 3/A=C ---> efficiency,
1/A+2/A+3/A = 1/2 ---> A+B+C=1/2.
A = 12,
B = 6,
C = 4.

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.

A = 2B, A = 3C.
So A = 2B = 3C.

A : B : C = (1/1) × 6 : (1/2) × 6 : (1/3)×6.
= 6 : 3 : 2.

A and B together do work in 2 days (Nowhere mention that A, B and C are doing simultaneously, so taking A and B as contains B and we have to find B alone).
So, Total work = (6 + 3) × 2 = 18
B can do alone = 18/3 = 6 days.

As the question says,

The time taken by A is twice that of B and thrice that of C, so
This means that;
Efficiency,
A=2*B=3*C

Efficiency is inversely proportional to the time taken to complete a task.

Time ratio
A/B=2/1,
A/C=3/1

So, the Efficiency ratio

A/B=1/2,
A/C=1/3
=>A/B/C=1/2/3.
A:B:C=1:2:3.

So in terms of RATIO,

Let 1-day work of A,B, C be 1unit, 2unit, 3unit.
i.e. work for A: 1 Day= 1 U---->eqn 1
work for B: 1 Day= 2 U----> eqn 2
Work for C: 1 Day= 3 U----eqn 3
Work for A+B+C: 1 Day= 6 U.
2 Day=12U----eqn iv
[Total work(12U) completes in Time =2days(given)
i.e.Total Works time taken by A+B+C, Time =2days]
Comparing (eqn ii & iv) find B can do the work alone
Work for B: 1 Day = 2 U ----> eqn 2
work for B: 3x2 Day = 6x2 U.
6 DAYS = 12 U.

B alone do the work in time = 6 days.

Simply:

6:3:1 = 9
9*2 = 18.

18/3 = 6.

2A = B.......eqn1.
3A = C.......eqn2.

A + B + C = 2days
A + 2A + C = 2days (from the eqn1),
A + 2A + 3A = 2days(from the run2),
6A = 2days ,
A = 2/6,
A = 1/3 days.

i.e A takes 3days to work.

We have B=2A.
B=2(3),
B=6.
That's B takes 6 days to complete.