Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. By the time when both of them clap simultaneously for the third time, how many times did Arun clap?
Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. By the time when both of them clap simultaneously for the third time, how many times did Arun clap?
The correct option is A 21
For Arun and Varun to clap together, the count has to be a multiple of both 3 and 7.
LCM of 3 and 7 is 21.
So, they will clap together every time the count reaches a multiple of 21.
The third time they clap together, the count will be 21×3=63.
We need to find the number of times Arun has clapped when the count reaches 63.
Now, every time the count reaches a multiple of 3, Arun claps. The counts at which he claps forms an AP with the first term as 3 and the common difference also being 3.
nth term of the AP =3+(n−1)3=3n
3n=63, or n=21
Hence, Arun would have clapped 21 times.
21
For Arun and Varun to clap together, the count has to be a multiple of both 3 and 7.
LCM of 3 and 7 is 21.
So, they will clap together every time the count reaches a multiple of 21.
The third time they clap together, the count will be 21×3=63.
We need to find the number of times Arun has clapped when the count reaches 63.
Now, every time the count reaches a multiple of 3, Arun claps. The counts at which he claps forms an AP with the first term as 3 and the common difference also being 3.
nth term of the AP =3+(n−1)3=3n
3n=63, or n=21
Hence, Arun would have clapped 21 times.
