Question

A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?

Answer 1

Let the two digits be x and x - 2

Given that the product of their digits is 8.

⇒ x(x - 2) = 8

⇒ 𝑥² - 2𝑥 - 8 = 0

⇒ 𝑥² - 4𝑥 + 2𝑥 - 8 = 0

⇒ 𝑥(𝑥 - 4) + 2(𝑥 - 4) = 0

⇒ (𝑥 - 4)(𝑥 + 2) = 0

⇒ 𝑥 = 4 𝑜𝑟 𝑥 = -2

Considering the positive value x = 4, x - 2 = 2.

∴ The two digit number is 42.