Question

a two digit number is such that the product of the digits is 20 if 9 is subtracted from the number its digits interchange their places find the number

Answer 1

Hi there.....
Here is the solution

let the two digits are X and Y
and the number is (10x+y)
then,
XY = 20 .........eq.(1)
also,
when 9 is substracted from the number
then,
(10x+y) -9 = (10y+x)
=>9x -9y -9 =0
=>x-y =1
=> x = y+1

now put this value in eq.(1)
(y+1)y =20
=>y^2 + y -20 = 0
=>y^2 +5y -4y -20 =0
=> y(y+5) -4(y+5) =0
=> (y+5) (y-4) =0
=> y = 4 or, y= -5
(1) here,
we consider +ve value
then, y= 4
and x = 4+1 =5

Hence the number is (10×5 +4) = 54

(2) here,
we consider -ve value of y
then,
y= -5
x = -5+1 = -4
Hence the number is
{10×(-4) + (-5)} = -45

Both answer is correct according to conditions given in the questions but the generally preferred answer is 54

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Hope it helps.......