Aptitude - Time and Work - Discussion

'A' is 30% more Efficient than 'B' that means


A --------- B
100% -------- 130%

to complete 100% of work 'A' took 23 Days i.e;
100% -----------------> 23 days.
130% -----------------> x days (need to find) 130% = (130/100) & 100% = (100/100).

By Cross Multiplying we get;

(130/100) *23 = x * (100/100).

=> x = (130/100) * (100/100) * 23.

=> x= (299/10) --------------------> This is the B value that we found now substitute these A and B values i.e

(A+B) = (1/23) + (10/299).

After Calculation we'll get;

(A+B) = (23/ 299) = 1/13,

Therefore Answer is 1/13.
That's It.

@Prathyusha.

Great, very helpful. Thanks.

As given, A=B+(30% of B) i.e. A=(13B/10).

And, A=1/23 so put this value in the above equation.
We get, B=(10/23*13).
Now find, A+B => 1/23+10/23*13.
=> 1/23(1+10/13).

After solving it the value of A+B is (1/13).

Efficiency of A=B+ (30/100) B (Efficiency of A is 30% more than B) =1/23.

A=B (1+30/100) =1/23.
B 13/10=1/23.
B=10/299.
If together A+B=1/23+10/299 =1/13.
Therefore the time taken is 13.

If efficiency = a : b = 13:10.
Then time = 10:13.
10 tends to 23.,
1 ratio equal to 23/10.
A and B working together = 23*23/10.

And I got 529/10.

Whether this method is right or wrong? Please, anyone, tell me.

@Chandradeepa.

Because it was given in the question that A is 30% more efficient than B.
So, we must consider A as 130% & B as 100%.

Why should we consider only 100 and 130?

FROM : @Abhishek - A does the work in 23 days and he is 30% faster also, so B will do that work in (23+ 30% of 23)= 29.9 days.

Now work done in 1 day by A= (1/23) and B=(1/29.9),
work done by A+B in one day = (1/23 + 1/29.9) = 1/13,

So the workdone by A+B will be in 13 days.

A is 30% more efficient than B.

That means A=130% speed B=100% speed assume, then convert into ratio format because 13:10 it's work, now we can convert to days 10:13 (this ratio for separate man work days)

We must now ratio formula then only we understand,
This method.
A:B=A:B.
Also we write A:B::A:B.

Now apply
10:13::23:X ( Formula A:B::c:d =>A*d=B*c ).

Now we can solve that,
10X=13*23.
X=(13*23)/10.
NNow we got X value X =299/10 days for B.
B 1 day work is 299/10.
Then as usually go next steps.

B = (10+13/23)12.
B = (23/23)13,
B = 13.