1.

The product of the digit of a two digit no. is 36 if 45 is subtracted from the no. its digits interchanged their places. Find the no.

Answer»

Let,
The TWO digit number be 10x+y
A/q,
X×Y = 36 ---------------------->(1)

Now,
10x + y - 45 = 10y + x
=> 10 x + y - 10y - x = 45
=> 9x - 9Y = 45
=> 9 ( x - y ) = 45
=> x - y = 45/9
=> x - y = 5
=> x = 5 + y ------------------------->(2)
Put the value of x in the equation (1),
We get,
( 5 + y ) . y = 36
=> y^2 + 5y - 36 = 0
=> y^2 + ( 9 - 4 )y - 36 = 0
=> y^2 + 9y - 4y - 36 = 0
=> y ( y + 9 ) - 4 ( y + 9 ) = 0
=> ( y + 9 ) ( y - 4 ) = 0
So,
y + 9 = 0 or, y - 4 = 0
=> y = - 9 => y = 4

Thus, y = 4
So,
(2) => x = 5+4
=> x = 9
Therefore,
The two digit number is
10×(9)+4
= 90+4
= 94


HOPE IT HELPS YOU......


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