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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
⇒ 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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