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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?

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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?

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Solution

Let the two digits be x and x - 2

Given that the product of their digits is 8.

⇒ x(x - 2) = 8

⇒ ๐‘ฅ2 - 2๐‘ฅ - 8 = 0

⇒ ๐‘ฅ2 - 4๐‘ฅ + 2๐‘ฅ - 8 = 0

⇒ ๐‘ฅ(๐‘ฅ - 4) + 2(๐‘ฅ - 4) = 0

⇒ (๐‘ฅ - 4)(๐‘ฅ + 2) = 0

⇒ ๐‘ฅ = 4 ๐‘œ๐‘Ÿ ๐‘ฅ = -2

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

∴ The two digit number is 42.

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Chapter 4: Quadratic Equations - Exercise 4.7 [Page 52]

APPEARS IN

R.D. Sharma Mathematics [English] Class 10
Chapter 4 Quadratic Equations
Exercise 4.7 | Q 22 | Page 52

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