Aarti and Rita can do a job in 8 hours and 12 hours, respectively. In how many hours can both do the job together?

Correct option is B

Given:

Aarti's time to complete the job = 8 hours

Rita's time to complete the job = 12 hours

Solution:

Rate of work for Aarti =$$\frac{1}{8}$$​ (since Aarti can finish the job in 8 hours)

Rate of work for Rita =$$\frac{1}{12}$$​ (since Rita can finish the job in 12 hours)

The combined rate of work when Aarti and Rita work together is the sum of their individual rates:

Combined rate =$$\frac{1}{8} + \frac{1}{12}$$​

Combined rate =$$\frac{3}{24} + \frac{2}{24} = \frac{5}{24}$$​

Thus, the time taken by both to complete the job together is:

Time taken $$= \frac{1}{\text{Combined rate}} = \frac{24}{5} = 4.8 \, \text{hours}$$​

So, Aarti and Rita can complete the job together in 4.8 hours.

Alternate Method:

Assume, Total Work = 24 unit (lcm of 8 and 12 )

Efficiency of Aarti = 3

Efficiency of Rita = 2

Thus, the time taken by both to complete the job together is:

= $$\frac{24}{2+3}=\frac{24}5$$ = 4.8 hours​