Question

<br /><br />3. Find the original number if the sum of digits and the number obtained by interchanging the digits are as<br />follows:<br />(i) 9,9 more than the original number<br />(ii) 7,27 more than the original number​

Answer 1

(1)

x +y = 9 ----------------------1

10x + y + 9 = 10y + x

9x - 9y = -9

9(x - y) = -9

x - y = -9/9

x - y = - 1 ----------2

solve both equations

x = 4

y = 5

the number is 45

(2)

x + y = 9------------------------------1

10x + y + 27 = 10y + x

9x - 9y = -27

9(x - y) = - 27

x - y = -3--------------2

solve both equations

x=3

y=6

the number is 36

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