A certain number between 10 and 100 is 8 times the sum of its digits and if 45 be subtracted from it the digits will be reversed. Find the number.
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Let the number between 10 and 100= 10x + y It 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 get x = 7 and y = 2. Therefore, the original number is 72.
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