The hands of a clock are 10 cm and 7 cm respectively. The difference between the distance traversed by their extremities in 3 days 5 hours is = ?

Answer: Option C

Number of rounds completed by the minute hand in 3 days 5 hours
$$\begin{array}{rl}& =\left(3\times 24+5\right)\\ & =77\end{array}$$
Number of rounds completed by the hour hand in 3 days 5 hours
$$\begin{array}{rl}& =\left(3\times 2+\frac{5}{12}\right)\\ & =6\frac{5}{12}\end{array}$$
∴ Difference between the distance traversed
$$\text{ = }\left[77\times \left(2\times \frac{22}{7}\times 10\right)-6\frac{5}{12}\times \left(2\times \frac{22}{7}\times 7\right)\right]\text{cm}$$
$$\begin{array}{rl}& =\left(4840-282.33\right)\text{ cm}\\ & =4557.67\text{ cm}\end{array}$$