Aptitude - Time and Work - Discussion

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).

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.

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.

As A is 30% efficient then B.
A = 13 work per day.
B = 10 work per day.
Total Work= 13 * 23 = 299.
No of days by (A & B) = 299/23 = 13.

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.

@Prathyusha.

Great, very helpful. Thanks.

'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.

A is 1 days's work is 1/23 which is given in the sum and B's 1 day's work we got. Add both then we get the result

Why we consider 10:13::23:x?

How 100:130 comes?