Aptitude - Time and Work - Discussion

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.

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.

Hi @Kiran.

If 6A = 2 then A = 3.

But you said it A = 12 give proper explanation?

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.

Another method.

Suppose C = X.

C = 2X then B = 3X, A = 6X.

Then B = 2X = 2*3 = 6 days.

If asked A = 6*3 = 18 days.

Let C takes x days to complete the work, then:

A, B, C.

3x, 3/2 x and x.

Their respective 1 day's work.

1/3x, 3/2x, 1/x now this is equal to 1/2 (as A+B+C takes 2 days to complete the work, thus their 1 day's work would be half).

Then we get x=4. Now 3/2 of 4 is 6.

How to comes the 1/x+2/x+3/x?

a=2b or a=3c.

=>b=a/2 , c=a/3.
Let us assume a=x.

Then,
a b c
x x/2 x/3

Therefore., (1/x + 2/x + 3/x) = 1/2.
6/x = 1/2.
x = 12.
B alone = x/2 = 12/2 = 6.

A can complete 1 unit/day.
B can complete 2 unit/day.
C can complete 3 unit/day.

Total works complete together by all in 1 days = 6 unit/day.

So, they complete in two days = 6X2 = 12 units.
So B takes 12/2 = 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.