Question

There is a number, the second digit of which is smaller than its first digit by 4, and if the number was divided by the digit's sum, the quotient would be 7.
Can you find the number?

Answer 1

Actualy, this puzzle has more than one answer. The numbers 62, 73, 84 and 95 will all satisfy the criteria laid out in the puzzle.

Perhaps the author meant to say, "if the number was divided by the sum of its digits, the quotient would be 7 and the balance would be zero". If that is the case, only one answer fits the bill. That is 84.

Answer 2

Let us solve it by trial and error
Let xy be the number
1st scenario
x= 5 then y= 1 ; 51 / (5+1) = 8,5
2nd scenario
x= 7 then y= 3 ; 73/ (7+3) = 7,3
3rd scenario
x= 8 then y= 4 ; 84/ (8 + 4) = 7

The number is 84

Answer 3

Usually we solve as under:let the digits be x and y. Then y=x-4 and N=10*x+y and N/(x+y)=7. Three variables three equations.By eliminating y we get N=11x-4 and N=14x-28. This leads to the solution x=8 and y=4. The solution is unique.