Aptitude - Time and Work - Discussion

Shortcut of these type of problems:

A&B = Difference * 'n' times / n^2 - 1.
= 60*3/3^2-1
= 180/9-1.
= 180/8=22.5 or 22 1/2.

Here A is thrice EFFICIENT than B.

A=1 B= 3
A takes 60days less than B to finish a work, This shows that if B takes to complete a work by "X" days. Then A will take X - 60 days to complete a piece of work.

We know that A=1.
B=3
A= X - 60
B= X (No.of day to complete a work).

Cross multiply: 3(X-60)=X => 3X-180=X,
-180=-2X => X= 90.

WORKING TOGETHER: A+B = 1/X-60 + 1/X.
We know that X = 90,
A+B = 1/90-60 + 1/90,
=1/30+1/90,
=(3+1)/90 => 4/90 => 2/ 45.

Therefore, A+B takes 45/2 days to complete a piece of work.
A+B = 22 1/2.

Since A finishes the job in 60 days less, from (ii) we get: 3X - X = 60.

A=30 B=90,
A+B=1/30+1/90.
=2/45.

A and B together can do the work in 45/2=22 1/2.

It is a good and clear method, Thanks @Prashant.

NO RATIO'S.

A is thrice as good as B.
This implies that if B take '' T '' days to complete the work, then A takes just ''T/3" days for same amount of the work.

Now coming to the second point in the question, A takes 60 days less than what B takes.

T/3 = T - 60.

----> T=90, ao B takes 90 days alone which implies A takes 30 days alone to complete work.

If A and B work together then no.of days required would be (1 / (1/30)+(1/90) ) which results in 22.5days.

A is thrice as good as workman as B so the ratio of time taken by A and B is = 1:3.
Let, A completed the work in x days.
B completed the work in 3x days.

A's 1-day work= 1/x and B's 1-day work= 1/3x,
So, A+B 's 1-day work= 1/x+1/3x,
=4/3x.

So, A+B completed the work in 3x/4 days.
Since,
A finishes a job in 60 days less than B.
therefore , 3x-x=60.
x=30.
therefore, Working together A+B completed the work in 3x/4 days.
= 3*30/4.
= 45/2.
= 22 1/2 days.

@All.

This is the easiest & shortest!.

Let a be x whereas b = 3x.
So, 3x " x = 60. x = 30.
therefore a = 30, b = 90.
so when they work together-> 1/30+1/60 = 4/90 = 2/45.

Together they can do the work in 22 (1/2) days.

Your explanation is easy, thanks @Showry.

3A = B.

If 60 is less than b(then 60 is two times of a)
then A=30,
b = 3 * 30 = 90,
a+b=1/30+1/90,
3*1/90+1/90,
(3+1)/90.

Where 4/90(to get days upside down).
90/4 = 22(1/2) days.

It's simply.
3a = b.