Question

a&b together finish a work in 24 days b alone takes 20 days more to do it than a alone,what time does a take to finish it alone​

Answer 1

Answer:

Apply the LCM method again

If B does 1/3rd of work in 12 days, then it will take 3*12=36 days to complete the work alone

Now take LCM of 36 and 24 i.e 72

So now the total work done will be 72 units

One day work of B will be 72/36=2 units

In 24 days, B does 2*24=48 units of work

Remaining work to be done is done by A i.e 72–48=24 units

So A does 24 units of work in 24 days

So one day work of A becomes 24/24=1 unit

Now if A alone has to complete the 72 units of work, then it takes 72/1=72 days

So The answer is 72 days

There is another approach to get this question done :-

B does 1/3rd of work in 12 days, so in 24 days, he does 1/3*2=2/3rd of the work

This means that on 24 days, A has done 1–2/3=1/3rd of the work

So if A takes 24 days to complete 1/3rd of the work, then it must take 24*3=72 days to complete whole work by himself

A word of advice,

Always go with the first method as it applies to every question in time and work whereas the second approach is short but only applies to this kind of questions.

Answer 2

Apply the LCM method again

If B does 1/3rd of work in 12 days, then it will take 3*12=36 days to complete the work alone

Now take LCM of 36 and 24 i.e 72

So now the total work done will be 72 units

One day work of B will be 72/36=2 units

In 24 days, B does 2*24=48 units of work

Remaining work to be done is done by A i.e 72–48=24 units

So A does 24 units of work in 24 days

So one day work of A becomes 24/24=1 unit

Now if A alone has to complete the 72 units of work, then it takes 72/1=72 days

So The answer is 72 days

There is another approach to get this question done :-

B does 1/3rd of work in 12 days, so in 24 days, he does 1/3*2=2/3rd of the work

This means that on 24 days, A has done 1–2/3=1/3rd of the work

So if A takes 24 days to complete 1/3rd of the work, then it must take 24*3=72 days to complete whole work by himself.

follow these steps and your question is done .