Time and work Quantitative aptitude question

[Q] If 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?
(a) 23 days
(b) 13 days
(c) 33 days
(d) 43 days

Solution

Answer   (b)
Explanation
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Work done by A in 1 day = 1/23

Let work done by B in 1 day = b

b × (130/100) = 1/23

=> b = 100/(23×130) = 10/(23×13)

Work done by A and B in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> A and B together can do the work in 13 days