a two digit number is such that its value is equal to four times the sum of its digits. If the digits are interchanged, the new number formed exceeds two thirds of the original number by 52. Find the number.

Answer 1

If the number is ab, then we are told that
10a + b = 4(a+b)
10b + a = 2/3 (10a+b)+52

Now just solve for a and b.

Answer 2

a=4
b=8
The original number is 48