Question
After swapping its digits, a two-digit number becomes
17 less than 200% of the original number. The sum of the digits is 8. Find the original number.Solution
Let tens = x, units = y. Original = 10x + y, swapped = 10y + x. 10y + x = 2(10x + y) − 17 ⇒ 10y + x = 20x + 2y − 17 ⇒ 19x − 8y = 17 … (I) x + y = 8 … (II) Multiply (II) by 8 and add to (I): (19x − 8y) + (8x + 8y) = 17 + 64 ⇒ 27x = 81 ⇒ x = 3 y = 8 − 3 = 5 Original number = 10×3 + 5 = 35
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