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