a no has 2 digit whose sum is 7 if adding 27 is added to the no its digit get interchange. find the number
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The 2 digit number is 25.
- Let the unit's place of the 2 digit number be a and the tens place of the 2 digit number be b.
- Now the number is b × 10 + a.
- Given sum of the digits is equal to 7
- Therefore a + b =7
- Now when 27 is added to the number the digits gets interchanged.
- That is the units place will be 'b' and the tens place will be 'a'
- Appling the given condition in equation
Original number + 27 = Interchanged number
10b + a + 27 = 10a +b
- Now we have 2 linear equations ,
a + b = 7 & 9a - 9b = 27
- On solving the equations we get a = 5 and b = 2
Therefore the number becomes 2 × 10 + 5 =25.
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