Correct option is (c) 68
Given the units digit of a two-digit number is 2 more than the tens digit. and the number is subtracted from the sum of the squares of its digits the result is two-thirds of the product of the digits.
Let the tens digit be x.x
Hence unit digit be x + 2.
Therefore the number will be 10x + (x + 2) = 11x + 2 ----(1)
Now,
x2 + (x + 2)2 − (11x − 2) = \(\frac{2x(x + 2)}3\)
2x2 + 4x + 4 − 11x − 2 = \(\frac{2x(x + 2)}3\)
6x2 − 21x + 6 = 2x2 + 4x
4x2 − 25x + 6 = 0
4x2 − 24x − x + 6 = 0
4x(x − 6) − 1(x − 6) = 0
(4x − 1)(x − 6) = 0
x = 41 and x = 6
Now as x has to be integer
Hence x = 6.
Thus number is 11x + 2 = 68