Question

A two digit number is such that the product of the digits is 8.When 18 is added to the number then the digits are reversed. what is the number?

Answer 1

Step-by-step explanation:

When 18 is added to the number, then the digits are reversed. The number is: 18 36 24 81.

Answer 2

Answer:Answer is 24.

Step-by-step explanation:

Let the two-digit number = “ xy ”

Where x takes the “tens” place and y, the unit. Hence you can write the two-digit no. “ xy” as “(10x + y)”.

Product of digits equals 8; x(y) = 8 …….(1)

Adding 18 to the number reverses the digits;

xy + 18 = yx Or (10x + y) + 18 = (10y + x)

This simplifies to; 9x + 18 = 9y …….(2)

Multiplying eq/n (2) through by “y” gives; 9x(y) + 18(y)= 9y(y)……(3).

Substituting in x(y) = 8 from eq/n (1) into (3) gives; 9(8) + 18y = 9y^2, which reduces to 8 + 2y = y^2. This is a quadratic eq/n whose solution for y equals 4 & -2. For y = 4, x = 2 by substitution into eq/n (1).

      Hence the two-digit no. xy = 24