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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

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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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