P is 30% more efficient than Q, How much time will they, working together, take to complete a job that P alone could have done in 23 days?

Correct option is B

Given:

P is 30% more efficient than Q.

P alone can complete the job in 23 days.

We need to find the time taken by P and Q working together to complete the job.

Formula Used:

Total Work = Efficiency × Time

Solution:

P can complete the job in 23 days.

Since P is 30% more efficient than Q, Q will take longer to complete the job.

Let the efficiency of Q be 100 units/day.

Then, the efficiency of P is 130 units/day (30% more than Q).

Efficiency of P = 130 units/day

Time taken by P = 23 days

Total work = Efficiency × Time = 130 × 23 = 2990 units

Efficiency of Q = 100 units/day

Combined efficiency of P and Q = 130 + 100 = 230 units/day

Time taken by P and Q working together:

Time  = $$\frac{2990}{230}$$​ = 13 days

P and Q working together will take 13 days to complete the job.