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# 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? - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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?

#### Solution

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.

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Solution 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? Concept: Solutions of Quadratic Equations by Factorization.
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