Aptitude - Time and Work - Discussion

Given A:B = 1:3 => B = 3A.'

Let assume A can complete work in x days which implies B = 3x
and also given B-A = 60 => 3x-x = 60 => 2x = 60 => x = (60/2) => 30

therefore A can complete the work in 30 days. and B can complete the work in 3*30 = 90 days
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 = 1.
x = 90/4 = 45/2 = 22 1/2.

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.

"A" is 3 times more than" B" (efficiency)

Difference = 60 days

3x-x = 60

X = 30days This is" B"

A=3 * 30 = 90 days.

So Total work =180

A=2 WORK
B=6 WORK

A+B TOGETHER CAN DO IN 180/8 = 22.5 DAYS.

A+B = (1/30 + 1/90) = 2/45.

How we are getting this?

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).

Let A's total work completion time be = n.
B's total work completion time = 3n,
Difference between B and A's daily work = 60.
3n - n = 60,
2n = 60.
n = 30.

Total daily work.
=1/3n + 1/n,
=1/90 + 1/30,
=2/45,
So total time to complete for both = 45/2 = 22.5.

a ------ b
x ------ 3x.

1/3 of the work is remaining = 1 - 1/3.
= 2/3.

2/3 of the work is completed by b = 60 days.
one of the work is completed by b = 60 * 3/2.
b = 90.
B one day work = 1/90.
A one-day work = 1/30.
a+b = 1/30 + 1/90.
a+b = 4/90
a+b = 2/45.

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

Thanks everyone.

Here a simple calculation is;
A takes 1 part and B takes 3 parts.
\
So A:B ratio is 1:3.
total 4p.and the difference is 2,they did work in 60 days so 60p.
4p=60.
p=15/1.
B total working days 15*3=45.
W/t is 45/2.

Thanks @Sundhar.