Question

6. The sum of the digits of a two digit number is 9. The number obtained by interchanging its digits is9 less than thrice the original number. Find the number.
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Answer 1

Given,

sum of digits = 9

Let x and y be the digits. Therefore, the actual number is 10x + y.

x+y=9 ..equ(1) [from given]

7x+7y=63 ...equ(2) [multiplying 7]

Interchanged number = 10y+x.

According to question,

10y+x= 3(10x+y) -9

» 10y+x=30x+3y-9

or, 29x-7y=9 ....equ(3)

Add equ 2 and 3.

» 36x = 62 .

or x = 62/36 = 1.7 = 2 (approx)

Therefore , y= 9-x=9-2 = 7 [from equ1]

The number is 27 [2(10)+7 =20+7 = 27]