Aptitude - Time and Work - Discussion

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.

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.

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.

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.

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 can do a work in 23 days.

So,
B can do a work in [ 23 + (30/100)*23] = 29.9 days or ~30 days.

Now,
A------------> 23 days.
B------------> 30 days.

LCM(23,30)= 690 (consider it as whole work).

Hence,
A can do 30 part of a work in 1 day.
B can do 23 part of a work in 1 day.

Therefore,
Both A+B can do 53 part of work in 1 day.
Hence, to finish whole work (i.e., 690) (A + B) will take (690/53) = 13.01 days or ~13 days

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.

Why can't we use ratio as A:B -> 70:100?

I think ratio taken may be wrong (100 : 130). it should be 130 : 100.

Please confirm it guys.

Shortcut and Easy Method.

A work - 100 % - 23
B work - 130 %.

130/100 * 23 = 299/10,
A + B 1 day work = 1/23 + 10/299,
13 + 10/299 = 23/299 = 1/13,
13 Days.