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Given:-Sum of the digits of a two digit number is 7 . After interchanging the digit new number formed is 45 more then the original number.

To Find:-The original number

Solution:-Let unit's digit be x

∴ ten's digit = 7-x

Original number = 10(7-x) + x

→ 70 - 10x + x

→ 70 - 9x

Number after interchanging its digits = 10x + 7 - x

→ 9x + 7

It is given that the number after interchanging its digits is 45 more than the original number. So, if we add 45 to the original number it will be equal to the number after interchanging its digits.

ACQ,

∴ 9x + 7 = 70 - 9x + 45

⟹ 9x + 9x = 70 + 45 - 7

⟹ 18x = 108

⟹ x = 108/18

⟹ x = 6

Original number = 70 - 9x

⟹ 70 - 9(6)

⟹ 70 - 54

⟹ 16

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