At a bridge construction site, there are two teams of workers, Team I and Team II. Each team has W workers. On a particular day, one worker is transferred from Team I to Team II. Now, if the amount of work done by Team I in (W + 1) hours and by Team II in (W + 2) hours is in the ratio of 10:12 respectively, what is the value of W?

Correct option is B

Given:
Number of workers in team I = W
Number of workers in team II = W
New number of workers in team I = W - 1
New number of workers in team II = W + 1
Formula Used:
Total work done = Number of workers × Time taken
Solution:
Total work done by (W - 1) workers in team I = (W - 1)(W + 1)
Total work done by (W + 1) workers in team II = (W + 1)(W + 2)
According to question,
$$\frac{(W - 1)(W + 1)}{(W + 1)(W + 2)} = \frac{10}{12} \\\Rightarrow \frac{W^2 - 1}{W^2 + 3W + 2} = \frac{5}{6} \\\Rightarrow 6(W^2 - 1) = 5(W^2 + 3W + 2) \\\Rightarrow 6W^2 - 6 = 5W^2 + 15W + 10 \\\Rightarrow W^2 - 15W - 16 = 0 \\\Rightarrow (W - 16)(W + 1) = 0 \\\Rightarrow W = 16 \text{ or } W = -1 \\\text{Since } W \ne -1, \text{ the solution is } \boxed{W = 16}$$​​