If A alone can complete a work in 90 days and B alone can complete the same work in 120 days, then which of the following statement(s) is/are correct?
I. Ratio of efficiency of A and B is 4:3.
II. Working together A and B can complete the same work in 30 days.

Correct option is D

Given:
A can complete the work in 90 days.
B can complete the work in 120 days.
Concept Used:

Efficiency is inversely proportional to the time taken to complete the work.
If A can complete the work in $$t_A$$​ days and B can complete the work in $$t_B$$​ days, then the ratio of their efficiencies is $$\frac{1}{t_A} : \frac{1}{t_B}$$.​
When working together, their combined work rate is the sum of their individual work rates.
Solution:
Efficiency of A $$E_A = \frac{1}{90}$$​ work per day.

Efficiency of B  $$E_B = \frac{1}{120}$$​ work per day.

$$E_A : E_B = \frac{1}{90} : \frac{1}{120}$$=$$\frac{360}{90}: \frac{360}{120}$$​​
$$E_A : E_B$$​= 4 : 3 
So, statement I is correct.
Combined efficiency $$E_{A+B} = E_A + E_B = \frac{1}{90} + \frac{1}{120}$$​​​

$$E_{A+B} = \frac{4}{360} + \frac{3}{360} = \frac{7}{360} \text{ work per day}$$​​
So, statement II is incorrect because A and B together take approximately 51.43 days, not 30 days.
Only statement I is correct. The ratio of efficiency of A and B is 4:3.