Aptitude - Time and Work - Discussion

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.

Lets assume that A completes the work in 'x' days.

B completes the same amount of work in 'x/2' days because A takes twice the time than B.

C completes the same amount of work in 'x/3' days because A takes thrice the time than C.

Now the work completed by A in one day is '1/x'.

Work completed by B in one day is '2/x'
Work completed by C in one day is '3/x'

All three together can complete the work in '2' days as given in the problem. So the work done by all three together in one day is '1/2'.

Hence the equation: '(1/x + 2/x + 3/x) = 1/2'.

Evaluating the above equation gives the value 'x=12' which is the number of days taken by A to complete the work.

As we know that number of days taken by B complete the work is 'x/2', we substitute the 'x' value.

Hence the evaluation '12/2' where 12 is the value of 'x'.

HENCE THE TIME REQUIRED BY B TO COMPLETE THE WORK IS 6 DAYS.

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.

Let's assume.
C takes 4 days to do X work.
B takes 6 days for the same X work.
A takes 12 days for the same X work.

so, efficiency
A = 1/12.
B = 1/6.
c = 1/4.

So, as they all together takes 2 days to work,

x/(1/12)+(1/6)+(1/4) = 2
From that, we got X ( total work ) = 1
So time taken alone by;
B = 1/(1/) = 6 days.

@All.

Here is the explanation for the answer.
As per the question, A=2B, A=2C.
equating, we get B = 3C/2,
A+B+C = 1/2.
Substitute the derived relations in the above equation, and the answer will be somewhere around 6.333333.
So, the correct answer is 6 days.

Hi @Kiran.

If 6A = 2 then A = 3.

But you said it A = 12 give proper explanation?

If C takes x days to complete a work A will take 3x days.

If B takes y days to complete a work A will take 2y days.

But 3x = 2y, so x = 2/3y.

As per ques, 1/2y+y+2/3y = 1/2.

Therefore y = 6.

B takes 6 days to complete the work.

As per given:

2A = B => A = B/2......(1).

3A = C......(2).

=> 3*B/2 = C......(2) (from 1st A = B/2).

(A+B+C)'s do the work in 2 days.

So (A+B+C)'s 1 day work is = 1/2.

Put the value of A and C from 1st and 2nd.

= (B/2+B+3*B/2) 's 1 day work = 1/2.

=> 6B/2, 1 day work = 1/2.

=> B's 1 day work = 1/2*2/6 = 1/6.

So B complete work in 6 days.

Let us consider the time taken by B is 2x.

So the time taken by A is "twice of B" then A=4x.

Similarly if time taken by B is x/2, the time taken by A is (2*x/2) = x; the time taken by C is x/3.

So the time taken by A is thrice of C (3* x/3). Hence we get x+x/2+x/3.

Since we consider work for one day we take inverse 1/x+2/x+3/x = 1/2.

In simple words:

A:B:C = 1:2:3 (Total 6 equivalent to A).

Now A, B and C together complete work in 2 days (i.e in 12 man days of A). So if A, B or C do the work alone, the required days would be:

A = 12 days.
B = 6 days.
C = 4 days.