A two-digit number is 3 more than 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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Solution
Let the digit in ones place be x and tens place be y Original number = 10y + x Number formed by reversing the digits = 10x + y Given 10y + x = 4(x + y) + 3 ⇒ 10y + x − 4x − 4y = 3 ⇒ 6y − 3x = 3 ⇒ 2y− x = 1 → (1) Also given that when 18 is added to the number the digits gets interchanged. Hence (10y + x) + 18 = 10x + y ⇒ 9x − 9y = 18 ⇒ x − y = 2 → (2) Add (1) and (2), we get 2y − x= 1 x − y = 2 --------------- y = 3 Put y=3 in x − y = 2, we get x − 3 = 2 ∴ x = 5 Hence (10y + x) = 10(3) + 5 = 35