Question

A clock has a 75 cm long second hand and a 60 cm long minute hand, respectively. In 30 minutes duration, the tip of the second hand will travel \(x\) distance more than the tip of the minute hand. The value of \(x\) in meters is nearly (Take \(\pi = 3.14\)):

• A. 139.4
• B. 140.5
• C. 220.0
• D. 118.9

Answer 1

The Correct Option is A

To determine the difference in distance traveled by the tips of the second and minute hands over 30 minutes, we will compute the circumference each hand traces and then calculate the disparity in their movements.

1. Calculate the circumference for each hand:

• The second hand measures 75 cm. Its circumference \(C_s\) for one full rotation is calculated as \(C_s = 2 \pi \times 75\). Using \(\pi = 3.14\), we find \(C_s = 2 \times 3.14 \times 75 = 471 \text{ cm}\).
• The minute hand measures 60 cm. Its circumference \(C_m\) for one full rotation is \(C_m = 2 \pi \times 60\). Consequently, \(C_m = 2 \times 3.14 \times 60 = 376.8 \text{ cm}\).

1. Calculate the distance covered by each hand in 30 minutes:

• The second hand completes 30 rotations in 30 minutes. The total distance \(D_s\) covered is \(D_s = 30 \times 471 = 14130 \text{ cm}\).
• The minute hand completes half a rotation in 30 minutes. The total distance \(D_m\) covered is \(D_m = 0.5 \times 376.8 = 188.4 \text{ cm}\).

1. Calculate the excess distance traveled by the second hand:

• The difference in distance, \(x\), is \(x = D_s - D_m = 14130 - 188.4 = 13941.6 \text{ cm}\).
• Convert this distance to meters by dividing by 100: \(x = \frac{13941.6}{100} = 139.416 \text{ meters}\).

Therefore, the value of \(x\) in meters is approximately 139.4 meters.