P is 30% more efficient than Q. If P alone can do some work in 20 days, then how long will Q alone take to do it?

Correct option is D

Given:
P is 30% more efficient than Q. P can do the work alone in 20 days.
Formula Used:
Efficiency ratio: If P is 30% more efficient than Q, then Efficiency of P: Efficiency of Q = 130:100 = 13:10. The time taken to complete the work is inversely proportional to efficiency.
Solution:
Since P is 30% more efficient than Q, the efficiency ratio of P and Q is 13:10. The time taken by P and Q to complete the work will be in the inverse ratio of their efficiencies. Thus, the time ratio of P and Q = 10:13. If P takes 20 days to complete the work, then: Time taken by Q = (13/10) * 20 = 26 days.
Alternate Method:
Let Q can complete the work in x days
So work done by Q in one day = 1/x
Work done by P in one day = 1/20
Then x×130/100=1/20
x= 100/(20×130)
x=1/26
Therefore, Q can complete the work in 26 days.