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Question
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
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Solution
Let 2-digit number = xy = 10x + y
Reversed digits = yx = 10y + x
According to question,
xy = 6
y = `(6)/x` ...(i)
and
10x + y + 9 = 10y + x
⇒ `10x + (6)/x + 9 = 10 xx (6)/x + x ...("From" (i) y = (6)/x)`
⇒ 10x2 + 6 + 9x = 60 + x2
⇒ 10x2 - x2 + 9x + 6 - 60 = 0
⇒ 9x2 + 9x - 54 = 0
⇒ x2 + x - 6 = 0
⇒ x2 + 3x - 2x - 6 = 0
⇒ x(x + 3) -2(x + 3) = 0
⇒ x = 2 or -3 ...(rejacting -3)
putting the value of x in (i)
y = `(6)/(2)` = 3
∴ 2-digit
= 10x + y
= 10 x 2 + 3
= 23.
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