Question

A salesman goes to New York every 15 days for one day and another every 24 days, also for one day. Today, both are in New York. After how many days will both salesmen be again in New York on the same day?

Answer 1

Answer:

Both salesmen will be in New York after 120 days.

Step-by-step explanation:

The L. C. M. of 15 and 24 is 120

Answer 2

After 120 days, both salesmen be again in New York on the same day.

A salesman goes to New York every 15 days for one day and another every 24 days, also for one day. Today, both are in New York.

We have to find the number of days when both salesmen be again in New York on the same day.

Let A and B are two salesmen. A goes to New York every 15 days for a day and B goes to New York every 24 days for a day.

         So there must be a day when they will be in New York on the same day. and that day is the least common mutliple of frequencies of days of both salesmen to go New York.

∴ both salesmen be in New York on the same day = LCM( 15 , 24) = 120

Therefore after 120 days, both salesmen be again in New York on the same day.