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in Linear Equations by (49.2k points)
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A two - digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

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Best answer

Let the one’s digit be ‘a’ and ten’s digit be ‘b’

Given, number is 4 times the sum of its digits.

10b + a = 4(a + b)

⇒ a = 2b -----(1)

Also, if 18 is added to the number, the digits are reversed.

⇒ 10b + a + 18 = 10a + b

⇒ a – b = 2 ----- (2)

Substituting a from eq1 in eq2

⇒ b = 2

Thus, a = 4

Number is 24

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