Jitesh and Kamal can complete a certain piece of work in 7 and 11 days, respectively, They started to work together, and after 3 days, Kamal left. In how many days will Jitesh complete the remaining work?

Correct option is B

Given:

Jitesh can complete the work in 7 days.

Kamal can complete the work in 11 days.

They work together for 3 days, after which Kamal leaves, and Jitesh continues working alone.

Concept Used:

The work done by a person in one day is the reciprocal of the number of days they take to complete the work.

Solution:

Work done by Jitesh in one day = $$\frac{1}{7}$$​​

Work done by Kamal in one day = $$\frac{1}{11}$$​​

Total work done together in 3 days:

​$$= 3 \times \left( \frac{1}{7} + \frac{1}{11} \right)$$​​

​$$= 3\times \left(\frac{11 + 7}{77}\right)$$​​

​$$= \frac{54}{77}$$​​

Remaining work after 3 days:

$$= 1 - \frac{54}{77} = \frac{77}{77} - \frac{54}{77} = \frac{23}{77}$$​​

Time taken by Jitesh to complete the remaining work:

$$= \frac{\frac{23}{77}}{\frac{1}{7}} = \frac{23}{77} \times 7$$​​

​$$= \frac{161}{77} \ \text{ days}$$​​

Alternate Solution: 

Total Work = LCM of (7, 11) = 77 

Efficiency of Jitesh = $$\frac{77}{7} = 11$$ 

Efficiency of Kamal = $$\frac{77}{11} = 7$$

Total work in 3 days = $$3 \times 18 = 54$$ 

Remaining work completed by Jitesh = 77 - 54 = 23 

​$$= \frac{23}{11} = \frac{161}{77} \ days$$​​