Q3 of 8 Page 54

The sum of the digits of a two–digit number is 11. The number got by interchanging the digits is 27 more than the original number. What is this number?

Let the digit in the unit’s place be ‘x’ and the digit in the tens place be ‘y’.


According to the question,


x + y = 11 … (1)


Then, the number = 10y + x = 11


The number got by interchanging the digits is 27 more than the original number


⇒ 10x + y = 10y + x + 27


⇒ 10x + y – 10y – x = 27


⇒ 9x – 9y = 27


Divide by 9 both sides


⇒ x – y = 3 … (2)


Equating equation (1) and (2)




x = 7


Put x = 7 in Equation (1)


7 + y = 11


y = 11 – 7


y = 4


∴ the number = 10y + x


= 10 × 4 + 7


= 40 + 7


= 47


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