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A two digit number is 3 more than 4 times the sum of its digits. If 18 is added tothe number, the digits are revered. Find thenumber.​

Answer»

Tens digit of the number be x ONE's digit be yOriginal Number = (10x + y)On reversing → (10y + x)ACCORDING to the question,10x + y = 4(x + y) + 3⇒ 10x + y = 4x + 4y + 3⇒ 10x - 4x = 4y - y + 3⇒ 6x = 3Y + 3⇒ 3y + 3 = 6x⇒ 3(y + 1) = 6x⇒ y + 1 = 2X ⇒2x - y = 1 ----- (Equation 1)Also,If 18 is added to the number, the digits are reversed.10x + y + 18 = 10y + x⇒10x - x + 18 = 10y - y⇒ 9x + 18 = 9y⇒ 9(x + 2) = 9y⇒ x + 2 = y⇒ x - y = -2 ----- (Equation 2)Subtracting Equation 1 and Equation 2, 2x - y = 1 (-) x - y = -2 x = 1 + 2∴ x = 3Substitute value of x in Any one of the equation.Here, let us substitute in Equation 2x - y = -23 - y = -2⇒y = 5We know that original number is of the form (10x + y)= 10(3) + 5= 30 + 5= 35So the required number is 35


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