In a two digit number, the digit at unit's place is equal to the square of the digit at ten's - Maths - Rational Numbers

Question

In a two digit number, the digit at unit's place is equal to the
square of the digit at ten's place, if 54 is added to the number
the digit gets interchanged Find the number

Varun.Rawat · Accepted Answer

Let the digit at tens place = xSo, the digit at units place = x2Now, original number = 10×x + x2 = 10x + x2Now, when the digits are interchanged, then new number = 10x2+xNow, according to question :10x + x2 + 54 = 10x2 + x⇒10x2 + x = 10x + x2 + 54⇒9x2 - 9x - 54 = 0⇒x2 - x - 6 = 0⇒x2 - 3x + 2x - 6 = 0⇒xx - 3 + 2x - 3 = 0⇒x - 3x + 2 = 0⇒x - 3 = 0  or   x + 2 = 0⇒x = 3  or  x = -2 rejectedSo, original number = 10×3 + 32 = 30 + 9 = 39

In a two digit number, the digit at unit's place is equal to the square of the digit at ten's place, if 54 is added to the number the digit gets interchanged. Find the number.