Question
On reversing its digits, a two-digit number becomes 78
less than 180% of the original number. Also, the difference between the digits is 2 (tens digit larger). Find the original number.Solution
Let tens = x, units = y. Original = 10x + y; swapped = 10y + x. 10y + x = 1.8(10x + y) − 78 1.8 = 9/5 ⇒ multiply by 5: 50y + 5x = 90x + 9y − 390 ⇒ 85x − 41y = 390 … (I) x − y = 2 … (II) ⇒ y = x − 2 Substitute in (I): 85x − 41(x − 2) = 390 ⇒ 85x − 41x + 82 = 390 ⇒ 44x = 308 ⇒ x = 7 y = 7 − 2 = 5 Original number = 10×7 + 5 = 75
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