Question

Shwetha comes to the swimming pool once every 12 days. Vinnie comes once every 4 days and Olga comes once every 10 days. Last Monday all of them were in the pool. In how many days all of them will meet at the swimming pool again? What day of the week will it be?

Answer 1

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

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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.