Alice can complete a task in 18 days, and Bob can complete the same task in 24 days. If they work together, how long will it take for them to complete the task?

Correct option is A

Given:

Alice = 18 days, Bob = 24 days.

Solution:
Combined time T$$=\dfrac{1}{\dfrac{1}{18}+\dfrac{1}{24}}.$$​​

T =$$\dfrac{1}{\dfrac{7}{72}}.$$​​

T=$$\dfrac{72}{7} =10\frac{2}{7}$$​ days

Alternate Solution:
Assume total work = LCM(18, 24) = 72 units.
Alice’s rate =$$\frac {72}{18}=$$​4 units/day; Bob’s rate $$= \frac{72}{24}=$$​3 units/day.
Together = 4+3=7 units/day

Time $$=\frac {72}7=10\frac{2}{7}$$days.