Aptitude - Time and Work - Discussion

***shortcut method******
D= no of days.
n= n times as fast.
D*n/n^2-1
60*3/3^2-1
180/9-1
180/8=90/4=22 1/2.

Can someone provide a solution for this problem using percentages or the efficiency ration ?

Let a did this work in X days.
B can do it in 3x days.


X+60=3x.
X=30.

It means A can complete this work in 30 days and B in 90 days;
Capacity of;
A is 3.
B is 4.
A+B= 4.

TIME =90/4.

The ratio of work done by A & B= 1:3.
(Because A is thrice as good as B)
A' s work done = Less than 60 days than B.
So take B's work done = x days---(1)
Then A's work done = x-60---(2)
So, 1=x-60,
3= x.

So cross mutiply as per the ratio simplification.
x * 1= 3(x-60),
x=3x-180,
3x-x=180,
x =90.

As per (1) & (2)
B's work done = 90 days,
A's work done = 90-60 = 30 days,
(A+B)'s 1 day work done = 1/30 +1/90=4/90=2/45,
Total work done = 45/2= 22 1/2 days.

3/2 *60, how come 3/2?

x : 3x.
3x - x = 60,
=> 2x = 60,
=> x = 30,
1/30 + 1/90,
= 4/90.
= 22 (1/2).

@All.

We can easily convert it to a linear equation.

Let B requires x days and forA it is y
it is given,x = 3y.

In the same way;
X-60=Y
By solving we have 2x- 180=0 :.x=90.
and y=90 - 60 = 30.

time diffence = 60days.
A is 3 times better then b.
That means A will do 3 times of work in day and B will do 1 time of A's work in 1 day
difference = 2 times.

Day difference = 60
1 time difference = 60/2 = 30.
A will do the work in 30 days.
B will do a work in 3*30 = 90days.

Thank you for very simple answer @Malleswari.

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.