Question

A two digit number is such that the product of its digit is 18 when 63 is subtracted from the number the digit interchange their places. Find the number

Answer 1

EXPLANATION:

here is your Answer:

Let the two digit number be 10x + y

Now, xy = 18 --- (i) and,

(10x + y) - 63 = 10y + x ---- (ii)

form (ii) we have,

10x + y - 63 = 10y + x=> 9x - 9y = 63=> x - y = 7 --- (iii)

Now,

(x - y)2 = (x + y)2 - 4xy

=> (x + y)2 = (x - y)2 + 4xy

= (7)2 + 4(18)

= 49 + 72

= 121

=> x + y = 11so, x - y = 7 and x + y = 11on adding we get,2x = 18 => x = 9 => y = 2Hence the two digit number is10(9) + 2 = 92

H O P E I T H E L P S Y O U

Answer 2

Answer:

Hope my answer is helpful for you.......

Let the digits be x and y

According to the question

x+y=18

Number=10x+y

: 10x+y=10y+x+63

10-x=63+10y-y

9x=63+9y

9x-9y=63

x-y=63/9

x-y=7..............................(1)

: now, xy=18

x=18/y....................(2)

Substituting the value of x in eq......(2)

18/y-y=7

-y²-7y+18=0

y²+7y-18=0

: the common factors are

y²+9y-2y-18

y(y+9)-2(y+9)

(y-2) (y+9)

y-2=0 OR y+9=0

y=2 y=-9

: x=18/y

x=18/2

x=9

Hence, the number is 92.......

Hope its helpful........