ICBSE 2MSowo-digit number is such thait thethe digits intenchange thei

1.	ICBSE 2MSowo-digit number is such thait thethe digits intenchange their piaces Find ithe mumberpoodaterf its digits is 20.i9is added to the numberICESE 2005
Answer» Solution - Let us assume x and y are the two digits of the two-digit number Therefore, the two-digit number = 10x + yand reversed number = 10y + x given - xy = 20 --------------1 and 10x + y + 9 = 10y + x ---------------2 Solve equation 2 10x + y + 9 = 10y +x 9y - 9x = 9 y - x = 1 y = 1 + x ---------------3 substitute equation 3 in equation 1 xy = 20 x (1 + x) = 20x^2+ x - 20 = 0 Solve this quadratic equation.... x^2 + 5x - 4x - 20 = 0 x(x + 5) - 4 (x + 5) = 0 (x + 5) (x -4) = 0 x = -5 and x = 4 As required number is positive two digit number, consider x = 4 Therefore, xy = 20 y = 20/x y = 20/4 = 5 therefore, the two digit number = 10x + y = 10*4 + y = 45. hit like if you find it useful

ICBSE 2MSowo-digit number is such thait thethe digits intenchange their piaces Find ithe mumberpoodaterf its digits is 20.i9is added to the numberICESE 2005

Answer»

Solution -

Let us assume x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + yand reversed number = 10y + x

given -

xy = 20 --------------1

and 10x + y + 9 = 10y + x ---------------2

Solve equation 2

10x + y + 9 = 10y +x

9y - 9x = 9

y - x = 1

y = 1 + x ---------------3

substitute equation 3 in equation 1

xy = 20

x (1 + x) = 20x^2+ x - 20 = 0

Solve this quadratic equation....

x^2 + 5x - 4x - 20 = 0

x(x + 5) - 4 (x + 5) = 0

(x + 5) (x -4) = 0

x = -5 and x = 4

As required number is positive two digit number, consider x = 4

Therefore, xy = 20 y = 20/x y = 20/4 = 5

therefore, the two digit number = 10x + y = 10*4 + y = 45.

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