How many times in 2015 did they exercise in the gym together?

Question

Sohan and Abhay did regular exercise in a gym at 4 pm on given days.
Abhay exercised every third day while Sohan only exercised on Thursdays.
They both started together on Thursday, 1st January, 2015.
How many times in 2015 did they exercise in the gym together?

Answer 1

Abhay's workout days in general = 3(n) + 1 where n is the number of gym days that he has completed.
Sohan's workout days = 7(n) + 1. n is the same as above.
This means Abhay will have 121 workouts and Sohan will have 52 workouts.
Now if we take the 1st day as the 0th day it becomes easy to understand. In this case Abhays days = 3n & Sohans days = 7n.
Now since both 3 and 7 are primes they will be working on the same day on the days described as below
3n × 7 or 7n × 3 or in other words on every day that is the multiple of 21. Now since 2015 is not a leap year and since we have taken the 1st day = 0th day, we have 364/21 = 17.333 days or 17 + 1{the first day} = 18 days where in both Abhay and Sohan workout together.