Firoz and Gangadhar can complete a certain piece of work in 18 and 11 days, respectively, They started to work together, and after 5 days, Gangadhar left. In how many days will Firoz complete the remaining work?

Correct option is D

Given:

Firoz completes work in = 18 days

Gangadhar completes work in = 11 days

Days worked together = 5 days

Formula Used:

Work Done = Efficiency × Days worked

Solution:

Total Work = LCM(18, 11) = 198 units

Efficiency of Firoz :

​$$\frac{198}{18} = 11 \text{ units/day}$$​

Efficiency of Gangadhar (EG):

​$$\frac{198}{11} = 18 \text{ units/day}$$​

Combined Efficiency ($$E_{F+G}$$​)

$$E_{F+G} = E_F + E_G = 11 + 18 = 29 \text{ units/day}$$​

Work = Combined Efficiency × Days worked together =29 × 5 = 145 units

Remaining Work:

Remaining Work = Total Work − Work done = 198 - 145 = 53 units

Time Firoz will take to complete the remaining work:

Days =$$\frac{\text{Remaining Work}}{\text{Efficiency of Firoz}} = \frac{53}{11}$$​

Converting into fraction of total work days:

​$$= \frac{53}{11} \times \frac{18}{18} = \frac{954}{198}$$​

Firoz will complete the remaining work in $$\frac{954}{198} \text{ days.}$$​