Aptitude - Time and Work - Discussion

I think the best and universal approach is this:

A can do the work in X days, B takes X+60 days for same work,
But (X+60)/X=3/1 as time taken by A and B is in 1:3 ratio,
Solving we get X=30,
A's one day work is 1/30,
B's one day work is 1/90,
combining their one day work we get 1/30+1/90=2/45,
total time taken by them is 45/2.

It's a clear explanation.

Thank you @Sheetal.

Please solve this question.

If the ratio of work efficiency of A and B is 3:2. If A and B together finish a work in 5 days in how much days B alone complete the work?

It is said A is 3 time as good as B.
ie. A=3*B
Again given,
A is able to finish a job in 60 days less than B.

say, B takes x days to complete 1 work
therefore A takes x-60 days to complete 1 work(same work)
A's 1 day work=1/x-60
B's 1 day work=1/x.
Substituting;

Applying in formula,
A=3B
ie. 1/x-60=3/x
so,x=90
x-60=30
so we got the number of days A alone and B alone worked i.e 60 and 90
1 day work of (A+B)=1 / 60 + 1 / 90 = 2/45,
So,nobr of days (A+B) worked = 45/2,
Answer is option B.

Yes, correct @Sugumaran.

The answer must be 45 days.

Let B does the work in x days.
Now let's think about A's efficiency.

As far as the question is concerned,
3*100/x =100/60.

So, x=180,
Efficiency of A+B=100/60+100/180,
= 20/9%.
So 20/9...........1
1..............9/20
100..........9/20*100 .
=45.

Let us understand this in a much simpler way.

Let the time taken by B to finish the work be X days.
Then according to the question Time is taken by the A is (X-60).
Work done by B in one day is (1/X),
Work done by A in one day is (1/X-60),

And we know that A is three times faster than B, So work done by A in one day is three times the work done by B in one day.

So 3*(1/X)=(1/X-60), 3X-180=X, X=90, Therefore B takes 90 days to complete the work hence A take 30 days to complete the work, therefore together they take 1/(1/30+1/90) days, which is equal to 45/2.

Thank you all.

a b
x 3x

2x=60 so x=30

total work=3*30=90
Ans=90/4=22 1/2.

Ratio of times taken by A and B = 1:3.

Means B will take 3 times which A will do in 1 time.
If difference of time is 2 days, B takes 3 days,
If the difference of time is 10 days, B takes (3/2) * 10 =15 days.

Can anyone explain me why the step 3/2*60 used. I couldn't get the logic of finding difference as 2.