Question

a two digit number is such that the product of its digit is 20. if9 is added to number, the digits interchange their places. find the number?

Answer 1

Hey Mate !

Here is your solution :

Let the ones digit is y.

and tens digit is x.

So,

Number = 10x + y.

A/Q,

=> Product of numbers = 20

=> yx = 20 --------------- ( 1 )

And,

=> 10x + y + 9 = 10y + x

=> 9 = 10y + x - 10x - y

=> 9 = 9y - 9x

=> 9 = 9 ( y - x )

=> 9 / 9 = ( y - x )

=> 1 = y - x

=> ( y - x ) = 1 ------------ ( 2 )

Using identity :

=> ( a + b )² = ( a - b )² + 4ab

=> ( y + x )² = ( y - x )² + 4yx

By substituting the value of ( 1 ) and ( 2 ),

=> ( y + x )² = ( 1 )² + 4 × 20

=> ( y + x )² = 1 + 80

=> ( y + x )² = 81

=> ( y + x ) = √81

=> ( y + x ) = 9 ----------------- ( 1 )

Adding ( 2 ) and ( 3 ),

=> y - x + y + x = 9 + 1

=> 2y = 10

=> y = 10 ÷ 2

=> y = 5

By substituting the value of y in ( 1 ),

=> yx = 20

=> 5x = 20

=> x = 20 ÷ 5

=> x = 4

Number = 10x + y

= ( 10 × 4 ) + 5

= 40 + 5 = 45

Hence , the required number is 45.

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Hope it helps !! ^_^