Chapter 4: Quadratic Equations

Example 10. A number consists of two digits whose product is 18. when 27 is subtracted from the number, the digits change their places. Find the number.

Solution:- Let the digit at unit place be x and the digit at ten’s place be y.

Number 10y + x

Reversed number = 10x + y

A/Q. 10y + x - 27 = 10x + y

Or, 9y - 9x = 27

Or, y - x = 3

y = x + 3 ------------- (i)

xy = 18 ----------------- (ii)

x(x + 3) = 18

Or, x² + 3x - 18 = 0

Or, x² + 6x - 3x - 18 = 0

Or, x(x + 6) -3 ( x + 6) = 0

Or, x = -6, 3

As digits ae never negative x = 3

From (i) y = x + 3

= 3 + 3

= 6

Number = 10y + x = 10 X 6 + 3

= 63