Aptitude - Time and Work - Discussion

A usually takes 23 days to finish the work and is 30% more efficient than B.
As per this,B should take = (130%) * (A) ------time to do work.
=> (130/100) * 23 => 1.3 * 23 ==> 29.9.

Now, (A + B) 1 day work = [1/23 - 1/29.9] = 1/13.
Therefore, A & B takes 13 days to finish the work.

Ais 30% more efficient than B.

Then their 1-day efficiency
A ----------B
130----------100
13---------- 10 (1-day work of A and B).

And total efficiency of A and B = 13 + 10 = 23
And time is taken by A and B together= A + B : A :: 23 : X.
(A + B)/A = 23/X (put the efficiency of A + B and A)
23/13 = 23/X (By solving it)
X = (23 * 13)/23 = 13days.

A is 30% efficient than B so A = 130%of B.
Ratio of work done by A and B =130:100 = 13 : 10,
Then time taken by A & B will be 10 : 13.
Given that 10x = 23 days (A takes 23days to complete the work)
x = 23/10.
Whole work done (w) = work done by (A + B) = (1/10x ) + (1/13x) = 1/x * ((23/130)
= (10/23) * (23/130) = 1/13.

So, in 13 days A and B can complete the work.

When A is 30% more efficient than B then,
B's efficiency = 100%.
A's efficiency =130%.

Now,
A takes 23 days to complete 1 or whole job.
A takes 1 day to complete 1/23 job.
According to the question,
130% = 1/23,
1% = 1/23 * 130,
100% = 1*100/23 * 130,
= 10/299 = B's 1-day work.

So, A + B together can do the work in 1 day = (1/23+10/299)
= 23/299 = 1/13.
They can do 1/13 part of the work in 1 day.
So, they can do 1 or whole part of the work in 13 * 1 = 13 days.
Ans: 13 days.

It is the most easiest process.
According to working ability A = 1.3 B.
So B= A/1.3.
So, A + B = A + A/1.3
= 2.3A/1.3
= 23A/13.
A does the in 23 days.
So, (23A/13) does the work = 23 * 13/23days.
= 13days.

A=30% more efficient than B.
Assume B = 1 so A = 1.3(one day work) So 23*1.3 = 29.9(total work).
a+b = 1+1.3 = 2.3.
==> 29.9/2.3 = 13 days.

A is 30% more efficient than B --A=1.3B.
A's 1 day work=1/23

Since A=1.3B
B's 1day work= 1/(1.3*23)=1/29.9.
A+B 's 1day work= (1/23+1/29.9)=1/13.
So 13 days.

Since A is more efficient, hence the ratio of time taken by A and B is 100:130 Or A:B = 10:13.

A alone can do the whole work in 23 days(time taken by A to complete the whole work)

Let time taken by B to complete the whole work be=x

Since time ratio is already with us, hence
23/x=10/13,
X=23 *13/10,

Hence
A 1day Work = 1/23,
B 1day work=10/23 * 13,

(A+B) 1day work=1/23 + 10/23*13,
(A+B) 1day work=(10+13)/23*13,
(A+B) 1day work=1/13.

Therefore (A + B) takes 13 days to complete the work if they work together.

Thanks @Nishant. Your answer is understandable.

Thank you @Pratyusha.