Aptitude - Time and Work - Discussion

A is thrice as good a workman as B:
So, A = 3 B.
Substitute A as 1/60.
1/60*3 = B.
1/180 = B
Working together :
A + B = 1/60 + 1/180.
= 4/180,
= 1/45 = 45 Days.

Let A complete work in = x days.
B will complete work in = 3x days.

(As a is 3x sufficient so b will take 3x much time)
Also, A take 60 days less,
So days were taken by B - 60 = days taken by A
So equation will be;
3x - 60 = x,
2x = 60,
x = 30.

So A completes work in 30 days and B in 30 X x = 90
A 1-day work = 1/30,
B 1 day work = 1/90,

1 day work of A & B together = 1/30 + 1/90 = 4/90.

If they both do 4/90 work in one day so to complete the whole 1 work they will take
4/90 X x = 1.
x = 90/4 = 45/2 = 22 1/2.

As A is thrice good than B then the Ratio of work done together is:

A : B
3 : 1

As A do work 60 days less than B , Suppose;
A : B
30 : 90---->LCM = 90,
(30×3)----->3u of A+1u of B =4u,
I.e 90/4 = 45/2 = 22(1/2).

A is thrice as good as workman as B and therefore can finish a job in 60 days less than B. Working together, they can do it in:

A = 3x, B= 1x ----> {1}
Here A's efficiency = 3.
B's efficiency = 1.

The Sum of their efficiency is 4 (we will need this later on).

According to the question:
A = 3x - 60.

Therefore 1 day's work of A and B is:
1/(3x-60) = 1/(x).
By solving we get x = 30
By putting the value of x in eqn {1}
We get A= 3 X 30 = 90 days.
B = 30 days.

By working together, they can do it in:
90/4 days.
By further solving, we get 22 1/2 days.

Assume B can do it in x days.
So A can in x/3 days.
x - x/3 = 60.
then x = 90.
So B can do the work in 90 days.
A can do it in 90/3 = 30 days.
A and B together can do it in 90 * 30/90 + 30 = 22.5 (Ans).

Given;

A = 3B;
A = B - 60.

Substitute A = 3B in 2nd equation(a=b-60).
3B = B-60
B = 30.

Therefore; A = 3B = 90.

A+B = (1/30 + 1/90) = 2/45.
So, the answer is 22(1/2).

I am not understanding this question.

Anyone help me to get it be explaining it along with the formulas?

First, A is thrice as good as B means.

If a takes a day to complete work, then b takes 3 days to complete the same work.

Here, time is inversely proportional to work.

So if b takes time T to complete, then a takes T/3 to complete.
In question, they mentioned that the time diff is 60 days.
So, T - T/3 = 60.
2T/3 = 60.
T = 90.
Now, calculate the combined work and how many days it will take.
1/30 + 1/90 = 2/45 = 22.5.

A is thrice of B and A takes 60 days less than B.
So,
Assume A takes - 30 days.
B takes - 90 Days.
One day's work of A- 1/30.
One day's work of B - 1 /90.
LCM = 90.
3/90 + 1/90 = 4/90.
90/4 = 22.5.

A : B is x : 3x.
A takes 60days less than B
So, 3x - x = 60.
X = 30.
Now Ais 30 and Bis 90.
Then the total work is 1/30 + 1/90
= 4/90 ==> 2/45.
So the answer ==> 45/2.
=> 22 1/2.