Suresh can finish a job in 10 days and Ramesh can finish it in 12 days. Calculate the fraction of the job that is remaining after they work on it together for 4 days.

Correct option is C

Given:

Suresh can finish a job in 10 days and

Ramesh can finish it in 12 days. C

They work on it together for 4 days.

Concept Used:

The rate of work of each person is the reciprocal of the time they take to complete the work. example,
A complete work in x day,
Rate of work in one day = $$\frac{1}{x}$$​ day

Solution:

Suresh can finish the job in 10 days, so his work rate is:

Suresh's rate = $$\frac{1}{10}$$

Ramesh can finish the job in 12 days, so his work rate is:

Ramesh's rate = $$\frac{1}{12}$$

Combined rate = $$\frac{1}{10} + \frac{1}{12}$$

= $$\frac{6+5}{60}$$

= $$\frac{11}{6}$$​​

Total Work Done in 4 Days: 

Work done = $$\frac{11}{60} \times 4$$​

 = $$\frac{44}{60}$$​

 = $$\frac{11}{15}$$

The work done from the total job,

Remaining work = $$1 - \frac{11}{15}$$​

 = $$\frac{15-11}{15}$$​

= $$\frac{4}{15}$$

So, the job remaining after 4 days is $$\frac{4}{15}.$$​​

Thus, the correct answer is (c).

Alternative Method:

4 day = 11 $$\times$$ 4 = 44

60 - 44 = 16

Remaining work = $$\frac{16}{60}$$

Remaining work = $$\frac{4}{15}$$​​