Question

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

Answer 1

The answer is 13 days.

Solution:-
Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work
=> 10 : 13 :: 23 : x
=> x  = 23 x 13 / 10 = 299/10


A's 1 day's work = 1/23

B's 1 day's work = 10/299

(A + B)'s 1 day's work = 1/23 + 10/299 = 23 = 1 /13

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

Answer 2

They, working together in 13 days 

BECAUSE

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.
Then, 10 : 13 :: 23 : x     =>     x =23 x 13/10  =>     x =299/10
A's 1 day's work =1/23
B's 1 day's work =10/299
(A + B)'s 1 day's work =1/23 + 10/299 = 23/299 =1/13


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