Aptitude - Time and Work - Discussion

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.

Finding the days for B and A:

The ratio difference is 2 and the day difference is 60.

So, for every single inc in ratio, it will increase by 30 days.

From this, we can say that A is 30 days and B is 90 days (1:3 time ratio).

A B
(x-60) x
B=3A;

x = 3(x-60);
x = 3x - 180;
2x = 180;
x = 90;
B = 90 days
A = 30 days.

Work done in 1 day A and B together => 1/30 + 1/90=2/45;
Whole work is will be done 45/2=>22 1/2;

A is thrice as good as workman as B and therefore can finish a job in 60 days - question
Just think A thrice is 90;
How means;

A is thrice as b;
For A assume as x;
then B assume as 2x;
then C assume as 3x;

in question they thrice -- so we can assume thrice as 3x;
if one is 30 means.
then twice as 60.
then thrice as 90.
So , one day of the work is 1/30, then thrice day of the work is 1/90.

Working together A+B;
1/30+1/90;then.
Then take lcm it will give 90.
Then check whether the 90 is in a and b
3+1/90;
4/90;
2/45;
Then reciprocal it or div it will give 22 1/2.

Given Equation
A = 3B ---> (i)
Let B=x days --> (ii)
Given:
A = x - 60 days ---> (iii)

Compare i and iii;
x-60 = 3B (i.e B=x).
x-60 = 3x,
x = 30.
A = 3 * 30 = 90 days.
B = 30 days.
LCM 90.
A's Efficiency 1.
b's Efficiency 3.
90/3+1 = 22 1/2 days.

A takes x-60 days.
B takes x days.
If A does work in 1 day then B takes 3 days.
So,
1/(x-60) = 1/x
Solving this we get x = 90
Now, A+B can do work in 1/90 + 3/90.
We get 45/2.

a : b
1 : 3.

And x-60:x

Then 3(x - 60) = x.
3x-180 = x,
2x = 180,
x = 90.

a = 90 - 60 = 30
b = 90
1\a + 1\b = 1\30 + 1\90 = 2\45.
a + b = 45\2.
So, the answer is 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 : B
1 : 3.

Difference = 2.
i.e 2 part = 60 (given),
1 part= 60/2 = 30.
A can do it in 30 days.
B can do it in 90 days.

A's 1 day's work= 1/30 and,
B's 1 day's work= 1/90,
A+B 1 day's work = 1/30 + 1/90 = 2/45.
They can do it in 45/2 days.

3x-x = 60,
x = 30.

A=90 B=30.

LCM(90,30) == 90unit.

for A -------> 1unit/day.
for B ------->3unit/day.

Total unit of work = 90/4 = 22.5.