Question

Four people clap after every 20 minutes, 30 minutes, 40 minutes and 50 minutes respectively. All of them clapped together at 10.00 am. Then they will again clap together at _______ .

• A. 3 pm
• B. 5 pm
• C. 6 pm
• D. 8 pm

Answer 1

The Correct Option is D

To solve this problem, we need to find the time when all four people clap together again after initially clapping at 10:00 am. This can be determined by finding the Least Common Multiple (LCM) of the intervals at which each person claps: 20 minutes, 30 minutes, 40 minutes, and 50 minutes.

Let's calculate the LCM: 

• Prime factorize each number:
  • 20 = 2² × 5
  • 30 = 2 × 3 × 5
  • 40 = 2³ × 5
  • 50 = 2 × 5²
• For LCM, take the highest power of each prime:
  • 2³: from 40
  • 3¹: from 30
  • 5²: from 50

Therefore, LCM = 2³ × 3 × 5² = 8 × 3 × 25 = 600 minutes.

600 minutes is equivalent to 10 hours (since 600 ÷ 60 = 10).

Now, add 10 hours to the initial clapping time of 10:00 am:

10:00 am + 10 hours = 8:00 pm.

Therefore, they will clap together again at 8 pm.