Question

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 1

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