John and Ling start their new jobs on the same day. John's schedule is 4 workdays followed by 1 day off. Ling's schedule is 7 workdays followed by 2 days off. On how many days during their first year of work (365 days) do John and Ling have the same day off?

Answer:16 days

Step-by-step explanation:

Given

John schedule is 4 Workdays and 5 th day off i. e. John take holiday at the 5 th day

Ling Work for 7 day and then took off on 8 th and 9 th day

i. e. after every 8 th and 9 th day he take off

So to find out common day off we nee take LCM of

i) 5 and 8

ii) 5 and 9

LCM (5,8) = 40 i. e. after every 40 th day they had same day off

and there are 8 such days in 365 days

LCM (5,9) = 45 i. e. after every 45 day they had same day off

and there are total of 8 days in 365 days

therefore there are total of 16 days in total out of 365 days