Nirbhay can complete a piece of work alone in 19 days and Vismay can complete the same piece of work alone in 6 days. They started the work together, but Nirbhay had to leave 4 days before the completion of the work. In how many days will the work get completed?​

Correct option is A

Given:

Nirbhay can do the work in 19 days

Vismay can do the work in 6 days

Nirbhay leaves 4 days before the work is completed

Solution: 

Let the total number of days the work takes be = D

LCM of total work to simplify the distribution of work. Assume total work = LCM of 19 and 6 = 114 units

Then, work per day:

Nirbhay = 114 ÷ 19 = 6 units/day

Vismay = 114 ÷ 6 = 19 units/day

Then Nirbhay works for (D − 4) days, and Vismay works for D days

Total work done = Nirbhay’s work + Vismay’s work

114 = 6(D - 4) + 19D

114 = 6D - 24 + 19D = 25D - 24

25D = 138

D = $$\frac{138}{25} = 5.52 \text{ days} = 5 \frac{13}{25} \text{ days}$$​​