Jitesh and Kamal can complete a certain piece of work in 18 and 17 days, respectively,They started to work together, and after 5 days, Kamal left. In how many days will Jiteshcomplete the remaining work?

Correct option is D

Given:

Jitesh completes work in 18 days

Kamal completes work in 17 days

Both work together for 5 days, then Kamal leaves

Find days Jitesh needs to complete remaining work

Formula Used:

Work done = Rate × Time

Solution:

Work done by Jitesh in 1 day = $$\frac{1}{18}$$​​

Work done by Kamal in 1 day = $$\frac{1}{17}$$​​

Work done together in 1 day = $$\frac{1}{18} + \frac{1}{17}$$​​

​$$= \frac{17 + 18}{18 \times 17} = \frac{35}{306}$$​​

Work done in 5 days together:

​$$= 5 \times \frac{35}{306} = \frac{175}{306}$$​​

Remaining work:

​$$= 1 - \frac{175}{306} = \frac{306 - 175}{306} = \frac{131}{306}$$​​

Time for Jitesh to finish remaining work:

​$$= \frac{\frac{131}{306}}{\frac{1}{18}}$$​​

​$$= \frac{131}{306} \times 18$$​​

​$$= \frac{131 \times 18}{306}$$​​

​$$= \frac{131 \times 18}{306}$$​​

​$$= \frac{2358}{306} \ days$$ 

Alternate Solution: ​

LCM of 18 and 17 = 306 units 

Jitesh’s rate = $$\frac{306}{18}$$​ = 17 units/day

Kamal’s rate = $$\frac{306}{17}$$​ = 18 units/day

Work done together in 1 day = 17 + 18 = 35 units

Work done in 5 days = 35×5 = 175 units

Remaining work = 306 - 175 = 131 units

Time for Jitesh to finish remaining work = \frac{131}{17} 

$$= \frac{2358}{306}$$​ days