Question

The product of the digits of a two number is 18. When 63 is subtracted from the number we get the two digit number with digits in the reverse order. a) If the digit in the tens place is x when what will be the digit in the one's place? b) Write the number using the place value of the digits. c) Form a second degree equation using the given condition d) Find the number​

Answer 1

Answer:

Let the number be 10x+y

According to question,

10x+y−63=10y+x

⇒10x−x+y−10y=63

⇒9x−9y=63

⇒x−y=7

⇒x=7+y (i)

xy=18 (ii)

Substituting the value of x in (ii) we get,

(7+y)y=18

⇒y

2

+7y−18=0

⇒y

2

+9y−2y−18=0

⇒y(y+9)−2(y+9)=0

⇒(y+9)(y−2)=0

⇒y=−9 and y=2

y=−9 is not valid

∴y=2

Putting the value of y in (i) we get,

x−2=7

⇒x=7+2

⇒x=9