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Sum of digits of a two digit number is 9. when the digits are interchanged ,the new number is greater than the original number by 9. find the original number. answer :45,54 |
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Answer» :We have to find the ORIGINAL NUMBER .Solution :Let units place digit be y and ten's place digit be X.Sum of digits of two digit number is 9.x + y = 9x = 9 - y ...1)Number formed : 10X + ywhen the digits are interchanged ,the new number is greater than the original number by 9. Reversed number : 10y + x10x + y + 9 = 10y + x10x - x + y - 10y = -99x - 9y = -99Y - 9x = 9Substituting value of x from Equation (1)9y -9(9 - y) = 99y - 81 + 9y = 918y = 9 + 8118y = 90y = 90/18y = 5Substituting value of y in equation (1)x = 9 - yx = 9 - 5x = 4So,Original number 10x + y := 10 × 4 + 5= 45⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━ |
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