Question

•Thisyear, John'sage is a multiple of 3. Last year, his age was 1 less than amultiple of 4. Next year, his age will be 3 more than a multiple of 5. What isthe youngest age he could be?

Answer 1

Given:

John's age is a multiple of 3

Let the age of this year = 3x

Last year, his age was 1 less than a multiple of 4.

So, {(3x-1) + 1 } is a multiple of 4

so, (3x) is a multiple of 4 also

And, Next year, his age will be 3 more than a multiple of 5

So, {(3x + 1 ) - 3 } is a multiple of 5

Considering the previous conditions:

The least multiple of 3 and 4 = 3 x 4 = 12

So, x = 12/3 = 4

Checking for the last condition:

$3x+1-3=12+1-3=13-3=10$

Which is the multiple of 5

So, the youngest age = 12 years