Question

Sum of the digits of a two digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number. Find the number. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Let the first digit of the number be "x", then the second digit will be 9 - x.

Then the number is, $(x\times 10)+(9-x)=9x+9$

When the digits are interchanged, then the new number is,

$(9-x)\times 10+x=90-10x+x=90-9x$

$90-9x=9x+9+27$

$\Rightarrow 18x=54$

$\Rightarrow x=3$

$\Rightarrow$ The number is 9x + 9 =9$\times$3+ 9=36.