Question

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

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

In man-hour problems, first convert team rates into \emph{individual} rates. Then:
Compute total work done in each phase.
Subtract from 1 (or total work) to find the remaining part.
Use the required time and remaining work to find how many extra workers are needed.

Answer 1

The Correct Option is B

Approach: Scale the whole job to a convenient number of "work units" so every per-member rate is a clean integer $-$ then it's pure counting, no fractions.

Step 1: Let the total job $=400$ units. A-member rate $=\dfrac{400}{200}=2$ units/h; B-member $=\dfrac{400}{400}=1$ unit/h; C-member $=\dfrac{400}{40}=10$ units/h.

Step 2: Opening crew rate $=2(2)+3(1)+1(10)=4+3+10=17$ units/h.

Step 3: In $23$ hours they do $23\times17=391$ units. Remaining $=400-391=9$ units.

Step 4: C leaves; the $2$ A $+\ 3$ B left produce $4+3=7$ units/h. To clear $9$ units in the next single hour, we need $9$ units/h $-$ short by $2$ units/h. Each extra B-member adds exactly $1$ unit/h, so $2$ more B-members close the gap.

Final answer: $2$ extra members from team B.