1.

product of digits of a two-digit number is 14 when 45 is added to the number then the digits interchange their places find the number

Answer»

Let the digits of the no. be x and y

So according to the question :

x × y = 14

xy = 14

Let the two DIGIT BO. be 10x + y

10x + y + 45 = 10y + x

10x - x + y - 10y = - 45

9x - 9y = - 45

9 ( x - y ) = -45

x - y = - 5

x = -5 + y

x × y = 14

-5 + y ( y ) = 14

-5y + y^2 = 14

y^2 - 5y - 14 = 0

y^2 - 7y + 2y - 14 = 0

y ( y - 7 ) + 2 ( y - 7 )

( y + 2 ) ( y - 7 ) = 0

y = - 2 ( neglected)

or

y = 7

we cannot take a negative value so we must take y = 7

xy = 14

x × 7 = 14

x = 14 / 7

x = 2

So the required no. is 27

Hope it helps you .


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