Question

Sum of the digits of a two digit number is 7. The difference between
original number and the number obtained by reversing the digits is
27. Find the original number.​

Answer 1

2x-10+(-10+2x) = 7

2x+2x-10+10 =7

4x

Answer 2

The original number is 52

Solution:

Given that sum of the digits of a two digit number is 7

Let the unit digit of original number be "a"

Then the tens digit is "7 - a"

The number formed by these digits = 10 x tens digit + units digit

The original number = 10(7 - a) + a = 70 - 9a

On reversing the digits, we obtain

tens digit = a

Units digit = 7 - a

The number obtained on reversing the digits = 10a + 7 - a = 9a + 7

Given that, difference between  original number and the number obtained by reversing the digits is  27

Hence we get,

70 - 9a - (9a + 7) = 27

70 - 9a - 9a - 7 = 27

63 - 18a = 27

18a = 63 - 27

a = 2

Thus the original number has tens digit = 7 - a = 7 - 2 = 5

The original number has units digit = a = 2

Therefore the two digit original number is 52

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