Jitesh and Kamal can complete a certain piece of work in 7 and 16 days, respectively. They started to work together, and after 2 days, Kamal left. In how many days will Jitesh complete the remaining work?

Correct option is A

Given:

Jitesh’s time = 7 days

Kamal’s time = 16 days

Both work together for 2 days

Then Jitesh alone completes the remaining work

Formula Used:

Work done = Rate × Time

Solution:

Jitesh's work rate = $$\frac{1}{7}$$​ work/day

Kamal work rate =  $$\frac{1}{16}$$​ work/day

Work done in 2 days by both:

​$$= 2 \times \left(\frac{1}{7} + \frac{1}{16}\right)$$​​

​$$= 2 \times \frac{23}{112} = \frac{46}{112} = \frac{23}{56}$$​​

Remaining work:

​$$= 1 - \frac{23}{56} = \frac{56 - 23}{56} = \frac{33}{56}$$​​

Time taken by Jitesh alone to finish remaining work:

Time = $$\frac{33/56}{1/7} = \frac{33}{56} \times 7 = \frac{231}{56}$$​ 

Alternate Solution: 

total work = LCM(7, 16) = 112 units

Jitesh’s rate = $$\frac{112}{7}$$​= 16 units/day

Kamal’s rate = $$\frac{112}{16}$$​= 7 units/day

Work done in 2 days by both:

$$= 2 \times (16 + 7) = 2 \times 23$$​ = 46 units

Remaining work = 112 - 46 = 66 units

Time for Jitesh to complete remaining work:

​$$= \frac{66}{16} = \frac{231}{56} \text{ days}$$​​

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