Answer: the numbers are 250 and 931
Explanation:
We have two numbers of 3 digits, A and B such that:
A/B = 3.724
A = 3.724*B
now we can divide the 3.724 in two parts
3.724 = 3 + 0.724
A = (3 + 0.724)*B = 3*B + 0.724*B
So, for now we want to find a number B of 3 digits (i will try to find the smallest possible value of B, because we need to multiplicate B by 3.724 to find A), such that:
0.724*B is an integer.
for example, we can start at B = 1000, and then we will start to reduce the value of B
0.724*1000 = 7240 is an integer, this is an even number, this means that we can take B = 500 and we still will get an integer number.
0.724*500 = 362.
Again, we have an even number, so we can take B = 250 and the result will be also an integer number.
0.724*250 = 181.
Ok, stop here, we can suppose B = 250, then we have:
A = 3.074*B = 3.724*250 = 931
Then the numbers are 250 and 931