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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
⇒ ๐ฅ2 - 2๐ฅ - 8 = 0
⇒ ๐ฅ2 - 4๐ฅ + 2๐ฅ - 8 = 0
⇒ ๐ฅ(๐ฅ - 4) + 2(๐ฅ - 4) = 0
⇒ (๐ฅ - 4)(๐ฅ + 2) = 0
⇒ ๐ฅ = 4 ๐๐ ๐ฅ = -2
Considering the positive value x = 4, x - 2 = 2.
∴ The two digit number is 42.
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