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4A certain number between 10 and 100 is 8 times the sum of its digit,and i 4 beshbrced tom htedigits will be reversed. Find the number |
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Answer» Let the number between 10 and 100 = 10x + yIt is eight times the sum of its digits⇒ 10x + y = 8(x + y)⇒ 2x - 7y = 0 ....(1) If 45 is subtracted from the number, the digits are reversed.(10x + y) - 45 = (10y + x)⇒ 9x - 9y = 45⇒ x - y = 5 .....(2)By solving equations (1) and (2), 7y/2 - y = 55y/2 = 5y = 2So x = 7we getx = 7 and y = 2.Therefore, the original number is 72. |
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