In a two digit positive number the unit digit is equal to the square of ten's place digit. The difference between the original number and the number formed by interchanging the digit is 54. What of 40% of the original number?

Let ten's place digit be a and unit's place digit be a²
Original number = 10 x a + 1 x a² = 10a + a²
The number formed by interchanging the digits,
New number = 10 x a ² + 1 x a = 10a ² + a
According to the question
(10a² + a) - ( 10a + a²) = 54
⇒ 10a² + a - 10a - a ² = 54
⇒ 9a² - 9a = 54
⇒ 9( a² - a) = 54
⇒ ( a² - a) = 54/9
⇒ ( a² - a) = 6
⇒ a² - a - 6 = 0
⇒ a² - 3a + 2a - 6 = 0
⇒ a (a - 3) + 2 (a - 3) = 0
∴ (a - 3) (a + 2) = 0
∴ a = 3, - 2
∴ Ten,s digit = a = 3
Unit's digit = a² = 3² = 9
Original number = 39
∴ Required number = 39 x 40/100 = 15.6