Question

The sum of a digit of a two digit number is 9. When we interchange, it is found that the resulting new number is greater than the original number by 27. What is the two digit number.​

Answer 1

Answer:

36

Step-by-step explanation:

x+y=9

10y+x=10x+y+27

9y-9x=27

y-x=3

(x+y)+(y-x)=12

y=6

9-y=x

x=3

10x+y= 36

Answer 2

Answer:

$\red { Original \: number }\green {= 36}$

Step-by-step explanation:

$Let \: tens place digit = x$

$Unit \:place \: digit = 9-x$

$Original \: number = 10x + 9 - x \\= 9x + 9 \:--(1)$

$If \: interchange \: the \: digits \:then \: the \\new \: number \: so \: formed = 10(9-x)+x \\= 90 - 10x + x \\= 90 - 9x \: ---(2)$

/* According to the problem given,

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

/* Divide each term by 9, we get

$\implies 10 - x = x + 1 + 3$

$\implies 10 - 1 - 3 = x + x$

$\implies 6 = 2x$

$\implies \frac{6}{2} = x$

$\implies x = 3$

/* Substitute x = 3 in (1) , we get

$\red { Original \: number } = 9x + 9 \\= 9\times 3 + 9 \\ = 27 + 9 \green {= 36 }$

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