Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively.

Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours.

The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

The correct answer is Option 2 (which is 2).

Let's solve this step-by-step by determining the individual work rates of members from each team.

Let the total job be represented as 1 unit of work.

Step 1: Calculate the work rate of one member from each team.

Team A consists of 5 members and takes 40 hours to complete the job.
Work done by Team A in 1 hour = $\frac{1}{40}$
Since there are 5 members in Team A, the work done by 1 member of Team A in 1 hour (${\mathrm{W}}_{\mathrm{A}}$) is:

${\mathrm{W}}_{\mathrm{A}}=\frac{1}{5\times 40}=\frac{1}{200}$ per hour.

Team B consists of 8 members and takes 50 hours to complete the job.
Work done by Team B in 1 hour = $\frac{1}{50}$
Since there are 8 members in Team B, the work done by 1 member of Team B in 1 hour (${\mathrm{W}}_{\mathrm{B}}$) is:

${\mathrm{W}}_{\mathrm{B}}=\frac{1}{8\times 50}=\frac{1}{400}$ per hour.

Team C consists of 10 members and takes 4 hours to complete the job.
Work done by Team C in 1 hour = $\frac{1}{4}$
Since there are 10 members in Team C, the work done by 1 member of Team C in 1 hour (${\mathrm{W}}_{\mathrm{C}}$) is:

${\mathrm{W}}_{\mathrm{C}}=\frac{1}{10\times 4}=\frac{1}{40}$ per hour.

Step 2: Calculate the work completed in the first 23 hours.

The initial group working for 23 hours consists of:
- 2 members from Team A
- 3 members from Team B
- 1 member from Team C

Combined hourly rate of this initial group:

$\text{Hourly Rate}=2\times {\mathrm{W}}_{\mathrm{A}}+3\times {\mathrm{W}}_{\mathrm{B}}+1\times {\mathrm{W}}_{\mathrm{C}}$

$\text{Hourly Rate}=2\times \frac{1}{200}+3\times \frac{1}{400}+1\times \frac{1}{40}$

Taking a common denominator of 400:

$\text{Hourly Rate}=\frac{4}{400}+\frac{3}{400}+\frac{10}{400}=\frac{17}{400}$ per hour.

Work done in 23 hours:

$\text{Work done}=23\times \frac{17}{400}=\frac{391}{400}$

Step 3: Calculate the remaining work.

$\text{Remaining Work}=1-\frac{391}{400}=\frac{9}{400}$

Step 4: Find the required additional members from Team B.

The remaining work needs to be completed in 1 hour.
After 23 hours, the member from Team C leaves.
Let $\mathrm{x}$ be the number of additional members from Team B required to replace the member from Team C.
So, the group working during the final 1 hour consists of:
- 2 members from Team A
- (3 + $\mathrm{x}$) members from Team B

Their total work done in 1 hour must equal the remaining work ($\frac{9}{400}$):

$2\times {\mathrm{W}}_{\mathrm{A}}+(3+\mathrm{x})\times {\mathrm{W}}_{\mathrm{B}}=\frac{9}{400}$

Substitute the individual work rates into the equation:

$2\times \frac{1}{200}+(3+\mathrm{x})\times \frac{1}{400}=\frac{9}{400}$

Convert $\frac{2}{200}$ to have the denominator 400:

$\frac{4}{400}+\frac{3+\mathrm{x}}{400}=\frac{9}{400}$

Multiply the whole equation by 400:

$4+3+\mathrm{x}=9$

$7+\mathrm{x}=9$

$\mathrm{x}=2$

Thus, 2 additional members from Team B are required to finish the job in the next one hour.