In a two digited number the sum of the two digits is 8. if 18 is added to the number its digits are

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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.

Let the tens and the units digits of the required number be x and y, respectively.Required number = (10x + y)10x + y = 4(x + y) + 3⇒10x + y = 4x + 4y + 3⇒ 6x – 3y = 3⇒ 2x –y = 1 ……….(i)Again, we have:10x + y + 18 = 10y + x⇒9x – 9y = -18⇒x – y = -2 ……..(ii)On subtracting (ii) from (i), we get:x = 3On substituting x = 3 in (i) we get2 × 3 –y = 1⇒ y = 6 – 1 = 5Required number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35

Hence, the required number is 35.

Concept: Pair of Linear Equations in Two Variables

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