Aptitude - Time and Work - Discussion

I am not understanding anything this, please explain.

A:B = 1:3
2p = 60
P = 30
30 : 90
1/30 + 1/90 = 2/45 = 22.5.

A is thrice as B, A:B=1:3.

B takes 60 days more than A to complete the work.

Lets consider A to complete the work in x days, therefore, B completes the same work in (x+60) days, x:(x+60).

Therefore,
As these are equally related to one and other;
1:3::x:(x+60).
Cross multiply we get x=30 days ie A can finish the work in 30 days,
Therefore B can do it in 90 days ie 3 times more days given.
Therefore:
(1÷30)+(1÷90).
= 22.5 days.

How come 4/90? I don't understand.

First thing, the work done is always same, i.e. Work done by A = work done by B = work done by A+B.

So, if A does a work in x days then B does it in 60-x days.

Now, we can write A=3B

So, work done by A will be = 1*x = x
Work done by B will be = 3*(60-x)

As we know work done remains same then

x = (60-x)*3.
x = 45,

So, A's total time = 45.
B's total time = 60-x = 60-45 = 15.

So, now we can find the total time taken by A+B to complete the work as,
1/15 + 1/45 = 4/45.

It's one day work of A+B so reciprocal it to get the total time taken by them.
45/4 = 22.5 days

(3-1)=2------>60
1------>30
3------->90.

1's day work for A= 1/30
1's day work for b=1/90
Both 1's day work=(1/30+1/90)
= 4/90.

Total day = 90/4.
= 22(1/2).
The answer is B.

We can simplify it.

Assume if B worked for 90 days and
C worked for 30 days.

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

A+B = 4/90 work.
ie, 90/4 = 22.5.

(T*T.D)/(T^2-1).

T-EFFICIENCY.
T.D-TIME DIFFERENCE.

So;
3*60/9-1 = 22.5.

Let's assume A completes its work in x days.

B completes in 3x days . since A is times efficient than B.
now, their difference is 60 days.
then, x-3x=60,
2x=60,
x=30,
A=30,B=90.

So, one days work of A and B together is A+B=1/30+1/90.
=4/90,
=2/45,
So one day work of A and B together is 2/45.
So A and B can complete the work in 45/2 days.
this equals to 22(1/2).

What is wrong with the below step?

A's 1-day work = 1/y.
Then, B's 1-day work = 1/3y.

Now,
A completes work before 60 days compared to B.

So,

1/y - 1/3y = 1/60
2/3y = 1/60
y = 40.

i.e., A completes in 40 days and B completes in 120 days,

Now, working together they complete in
1/A + 1/B = 1/40+ 1/120 = 1/30.

So, Together they complete in 30 days.