Aptitude - Time and Work - Discussion

Hi, friends.

We know that A capability to do work is 3 times of B,ok
Then the the ratio of Efficiency is A:B=3:1

And the ratio of time (days) is A:B=1:3 ...(The ratio get reverse because Efficiency and time are inversely proportional)

Now,
Time taken by A to complete work = (X) day &
Time taken by B to complete work = (X+60) day.

*We compare the ratio of time
(X/X+60)=(1/3) get X = 30 ----> (1).

From (1) we get A need 30 Days and B need 90 days
Now take lcm of (A day and B-day).

That is LCM of (30 & 90).

A & B need to complete 90 work.

So, the efficiency of A is (3 w/d) & B's efficiency (1w/d).
When they together (A+B) = work done is (4w/d).
So (90w/(4w/d)) = 22 1/2.

A:B = 1 : 3.

Let's say A's work is x, then x : 3x.
Now, 3x - x = 60.
Given in question.
2x = 60, x = 30
Now,A = 30, B = 90.

So, let's take the ratio as 3:1.
Consider b - 60 = a.
3a - 60 = a,
A = 30,
30 = b-60,
B = 90.
A + b = 1/30 + 1/90.
= 2/45.
Which is 45/2=22.5=22 1/2.

A = 3B;
A time : x-60; B time =x;

In 1 day together work =1/(x-60) +1/x.
And we also know (x-60)/x = 1/3;
From this two got x = 90 and time from eq 1 is 22.5.

A = 3B
Suppose workdone in 1 day by 'B'= 1/n.
Suppose workdone in 1 day by 'A'= 1/(n-60).
We get eqn;
1/(n-60) = 3(1/n).

So, n =90 days (Time taken by B to complete the work).
A= 30 days.
A+B = (1/30)+(1/90) = 22.5.

A:B = 1:3.
B = 3A.
Difference is 60days,
therefore B - A = 60,
3A - A = 60,
2A = 60,
A = 30 & thus B = 90.

Now, 1/30 + 1/90 = 22.5.

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.

@Harsha

You gave a very good explanation, thank you.

Thank you all for explaining.

If A completes the work in x days, B will do the same in 3x days.

3x - x = 60.
2x = 60.
Then x = 30 and 3x = 90.
(A + B) 's 1 day's work.
=1/30 + 1/90.
= 4/90.

So, A and B together will do the work in;

= 90/4.
=>22 and 1/2.