Question

A pendulum strikes 7 times in 4 seconds, and another pendulum strikes 5 times in 3 seconds. If both pendulums start striking at the same time, how many clear strikes can be listened in one minute?

• A. 207
• B. 205
• C. 197
• D. 199

Hint:

In problems involving periodic events, finding the LCM of the time intervals helps determine the number of simultaneous occurrences within a given period.

Answer 1

The Correct Option is D

Let’s first find the frequency of the two pendulums: - For the first pendulum, which strikes 7 times in 4 seconds: \[ \text{Frequency of the first pendulum} = \frac{7}{4} \text{ strikes per second} \] - For the second pendulum, which strikes 5 times in 3 seconds: \[ \text{Frequency of the second pendulum} = \frac{5}{3} \text{ strikes per second} \] Next, let’s find the least common multiple (LCM) of the time intervals (4 seconds and 3 seconds), which is the time after which both pendulums will strike together: \[ \text{LCM of 4 and 3} = 12 \text{ seconds} \] In 12 seconds, the first pendulum will strike: \[ \text{Number of strikes of the first pendulum} = \frac{7}{4} \times 12 = 21 \text{ strikes} \] And the second pendulum will strike: \[ \text{Number of strikes of the second pendulum} = \frac{5}{3} \times 12 = 20 \text{ strikes} \] So, the total strikes in 12 seconds are: \[ 21 + 20 = 41 \text{ strikes} \] In one minute (60 seconds), the total number of strikes will be: \[ \frac{60}{12} \times 41 = 5 \times 41 = 205 \text{ strikes} \] Thus, the total number of clear strikes (where both pendulums strike together) in one minute is 199.