Answer:
60 days, Friday
Step-by-step explanation:
This problem is solved using concept of LCM.
LCM is the least number which is the common multiple of given set of different number.
To find the LCM we method of prime factors, the steps are given below
- get all the all the prime factor of the given set of number
- select all the prime factors as many times they occur in given set of number
- multiply together the numbers selected together to get LCM
________________________________________________
Given
frequency of visiting swimming pool by Shwetha = once in 12 days
factors of 12 = 2 * 2 * 3
frequency of visiting swimming pool by Vinnie = once in 4 days
factors of 2 = 2 * 2
frequency of visiting swimming pool by Olga = once in 10 days
factors of 10 = 2 * 5
minimum no of days after which they will be visiting together will be least common multiple of number of days after which they visit swimming pool individually.
Selecting the prime numbers with their highest occurrence
we have 2, 2, 3 ,5
multiplying them together we have
2 * 2 * 3* 5 = 60
therefore 60 is the LCM of 12, 4, 10
it means that Shwetha, Vinnie and Olga will visit swimming pool together once in 60 days
It is given that they visited on Monday and now they will visit after 60 days again.
since in one week there are seven days, every eighth day will be monday
so we divide 60 days by 7 to see how many cycles of monday has passed.
60/7 = 8 4/7
It suggest that 8 weeks has passed and they will meet on 4 days after Monday which will be Friday.
Thus they will meet meet at the swimming pool again in 60 days.
It will be Friday.
