Question

The sum of the digits of a two digit numbers is 7. If we add 45 to the number, the
digits are interchanged. Find the number.
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Answer 1

Let ,

Ten's digit of a number = " x "

Unit's digit of a number = " y "

Number = " 10x + y "

According to the question ,

x + y = 7 --- (i)

and

10x + y + 45 = 10y + x

9x - 9y = -45

x - y = -5 --- (ii)

Adding eq (i) and eq (ii) , we obtain

x + y + x - y = 7 + (-5)

2x = 2

x = 2/2

x = 1

Put x = 1 in eq (i) , we get

1 + y = 7

y = 6

∴ The number is 16