Question

The units digit of a two-digit number is 2 more than the tens digit. If the number is subtracted from the sum of the squares of its digits the result is twothirds of the product of the digits. What is the number ?

(a) 62

(b) 58

(c) 68

(d) 86

Answer 1

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