SShwetha comes to the swimming pool once every 12 days. Vinnie comes once every 4 days and Olga comes every 10 days. Last monday all of them were in the swimming pool. in how many days will all of them meet at the swimming pool again? What day of the week will it be/
Answers
Given :
Shwetha comes to the swimming pool once every 12 days
Vinnie comes to the swimming pool once every 4 days
Olga comes every 10 days.
At Last Monday all of them were in the swimming pool
To Find :
( a ) In how many days will all of them meet at the swimming pool again
( b ) What day of the week will it be
Solution :
∵ Shwetha comes to the swimming pool once every 12 days
Vinnie comes to the swimming pool once every 4 days
Olga comes every 10 days.
Now,
( a )
They will meet again on = LCM of ( 12 days , 4 days , 10 days )
Or, Factor of 12 = 2 × 2 × 3
Factor of 4 = 2 × 2
Factor of 10 = 2 × 5
So, The LCM of ( 12 days , 4 days , 10 days ) = 2 × 2 × 3 × 2 × 5
Or, = 120
So, They will meet again after 120 days
( b )
If they meet on Monday ,
∵ In 120 days , total weeks = 17
total day = 1
So, As Today is Monday , then after 17 weeks , day come = Monday
and 1 more day = Monday + 1
= Tuesday
So, The day of week = Tuesday