Question

Write a pair of numbers such that the value of the 7 in the first number is 1000 times the value of the 7 in the second number, and the value of the 3 in the first number is 100 times the value of the 3 in the second number

Answer 1

If I get it right, then we could find for example those pairs of numbers:

70300 vs 10073
37000 vs 10307
70003000 vs 1007003
3070000 vs 1030070
370000 vs 103070

Answer 2

As infinitely many such possible number pairs can be formed, one of the instances of such pair would be (37000 and 307).

Solution-

Suppose the former one is aaaaa and the later one is bbbbb.

The value of 7 in the former is 1000 times greater than in the later, so let's make it 7000 and 7.

Then the numbers will be in the following form,

a7aaa and bbbb7

Again, the value of 3 in the former is 100 times greater than in the later.

Then the numbers will be in the following form,

37aaa and bb3bb7

Substituting all the a's and b's by 0,

we get, 37000 and 307 is a possible set. Replacing 0 with any number from 1-9, will yield another number pair which will satisfy the conditions.