Question

251.
A two digit number is such that the product of the digit is 8 when 18 is added to the number digits are
reversed. The number is:
(a) 18
(b) 24
(c) 81
IdY​

Answer 1

24

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Answer 2

Answer:

b) 24

Step-by-step explanation:

Let the two digit number = (10x + y)

Given xy= 8.........9(1)

Also, (10x + y) +18 = (10y + x)

: 10x - x + y - 10y = - 18

9x - 9y = -18

x-y = -18/9

x-y = -2

⇒x= y-2.........(2)

substitute(2) in (1)

xy = 8

:(y-2)y = 8

: $y^{2}$-y-8= 0

:$y^{2} -4y +2y -8 =0$

:y(y-4)+2(y-4)=0

:(y-4)(y+2)=0

: y= 4, -2

since y cannot be negative, y=4

from (1), xy =8

            :x X 4 = 8

            : x= 8/4=2

⇒the two digit number = (10x + y)= 10 X 2 + 4 =24