Mathematics
If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is :
46
64
56
48
Quadratic Equations
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Answer
Let x be ten's digit and y be unit's digit.
Given,
Product of digits of number = 24
⇒ xy = 24 ………(1)
Number = 10x + y
Given,
If 18 is added to a two-digit number, its digits are reversed.
⇒ 10x + y + 18 = 10y + x
⇒ 10x - x = 10y - y - 18
⇒ 9x = 9y - 18
⇒ 9x = 9(y - 2)
⇒ x = y - 2 ………(2)
Substituting value of x from Eq. (2) in Eq. (1), we get :
⇒ (y - 2)y = 24
⇒ y2 - 2y = 24
⇒ y2 - 2y - 24 = 0
⇒ y2 - 6y + 4y - 24 = 0
⇒ y(y - 6) + 4(y - 6) = 0
⇒ (y + 4)(y - 6) = 0
⇒ y + 4 = 0 or y - 6 = 0
⇒ y = -4 or y = 6.
Digit cannot be negative, so y = 6.
⇒ x = y - 2 = 6 - 2 = 4.
Number = 10x + y = 10(4) + 6 = 40 + 6 = 46.
Hence, Option 1 is the correct option.
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