A two digit number is such that the product of its digit is 18. When 63 is subtracted from the number the digits interchange thier places. Find the number.
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Step-by-step explanation:
let the Units place be x and Tens be y
By the given statements
xy=18...........(1)
10x + y - 63 = 10 y + x
9x - 9y - 63= 0
9x - 9y = 63
x-y = 7..........(.2)
x= 7+y
put value of x in eq 1, we get
( 7+y ). y = 18
y² + 7y = 18
y² +7y-18=0
y² +9y -2y -18= 0
y(y+9) -2 ( y +9) =0
( y+9) (y-2). = 0
y=-9 , y = 2
y= 2........
so, x= 7+2=9
therefore the two digit number is 10(9)+2
= 92
mayankanand73:
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