A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. find the number.
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so your answer is 35
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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 = 3 On substituting x = 3 in (i) we get 2 × 3 –y = 1 ⇒ y = 6 – 1 = 5 Required number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35 Hence, the required number is 35
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