Aptitude - Time and Work - Discussion

Simple method:

Say B completes the work in 'x' days.

Then A will take (x-60) days to finish the work.

Since A is thrice as good as B, 3A=B.

Therefore, 3 (x-60) =x, x=90.

B's 1 day work=1/90, A's 1 day work=1/30.

(A+B) 's 1 day work= (1/90+ 1/30) =2/45.

Therefore, both can finish the work in 45/2 days i.e., 22 1/2.

A is twice as good as workman B and together they finish a piece of work in 14 days. A alone can finish the work in.

Did they mention that difference of working time is 60 days.

In the given question the ration of capacity of work in day a:b is = 3:1.

So always inverse proportion to capacity and work like the way a and b can do the work ration =1:3 i.e. a's one day work = b's three days work.

So let now finish work together is imagine x.

Ratios of each person a's work = x* 1/4 = X/4. (1).

Ration of b's work = x* 3/4 = 3X/4. (2).

In the given question difference is 60 days.

So 3X/4-X/4 = 60 Days.

Solove ther x we get x = 120.

Now substitute x in (1) and (2).

W e get a's part of one day work = 30 days.

And b's part of one day work = 90 days.

Now solve the.

A and B together work = 1/30+1/90 = 4/90 =2/45.

This is and b together part of work now one day work = 45/2 = 22.5 days.

Why so many stories I don't know.

Its as simple as this:

A's 1 day's work = x.

B's 1 days work = x+60.

So, total one day's work is.

1/x + 1/x+60 = 1.

And you get x = 30 that is total days required for A to cmplete the work where B's value gets 90 days.

Rest you can solve.

X - 3X = 60.

X = 30.

A done works 30 days and B done the work 90 days.

A work done in 1 day 1/30 part.

B work done in 1 day 1/90 part.

A and B work together in 1 day (1/30+1/90) = 2/45 part.

Time taken in this work 22.5 days.

Ratio of times taken by A and B to finish a work is 1 : 3.
A:B=1:3 OR A/B=1/3 or 3A=1B --(1).

B-A = 60.
B-(1/3)B = 60 (Substituting the value of A from eq 1).
3B-B = 180 (Multiply through by 3).
2B = 180.
B = 180/2.
B = 90.
A = (1/3)*90.
A = 30.

So, A can do the job in 30 days.
Therefore, A can do 1/30 of the job per day.

And B can do the job in 90 days.
Therefore, B can do 1/90 of the job per day.

Work they can do per day:
= (1/30) + (1/90).
= (3/90)+(1/90).
= (3+1)/90.
= 4/90.

So the job will take 90/4 days, which is 45/2 or 22.5 days.

A can do the job in x days.
B can same job in 3x days.

3x=x+60 by B.
x=30.

One day work by A and B = 1/30+1/90 = 4/90 = 2/45.

Whole job done by A and B = 45/2 = 22.5 days.

How do we get 4/90 ?

Hi @Michael,

By taking the L.C.M of 30 & 90 you'll get 90.

Now, here the value become.

=1/30+1/90.
=(3+1)/90.
=4/90.
=2/45.

So, 2/45 is total work done by them,
But we've to find the days.

By formula work to days.

N work = 1/N days.
So, 2/45 = 45/2 days.

Answer = 22.5days.