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Eight times a two digit number is equal to three times the number obtained by reversing the order of its digits .if the difference between the digit is 5 ,find the number.

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Let the number be A B its value is 10 A + B

Reverse of the number BA it s value is 10 B + A

given 8 * (10A +B) = 3 (10 B + A )

80 A + 8 B = 30 B + 3 A

77 A - 22 B = 0

7A - 2 B = 0 =>__ 2B = 7A__

we know that B is between 0 and 9. A is between 0 and 9

B and A are not zeros.

**A has a factor 2 **and* B has a factor 7* for the above equation to be true. **There is no other way.**

There is only one such possibility : A = 2 and B = 7

The number is 27.

__To solve this we do not need the second data, that is, difference between the digits is 5. This information is not needed.__

Reverse of the number BA it s value is 10 B + A

given 8 * (10A +B) = 3 (10 B + A )

80 A + 8 B = 30 B + 3 A

77 A - 22 B = 0

7A - 2 B = 0 =>

we know that B is between 0 and 9. A is between 0 and 9

B and A are not zeros.

There is only one such possibility : A = 2 and B = 7

The number is 27.