Question

Sum of two digits of a two digit number is 9 when we interchange the digit it is found that the resulting new number is greater than the original number by 27 what is the two digit number

Answer 1

$\text{Let the two digit number be 10a + b}$

$\Rightarrow According\:to\:the\:question =>a + b = 9 [==>Equation 1]$

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$\text{Let the two digit number after interchanging the digits be 10b + a}$

ATQ

$10b + a - (10a + b) =27$

$9b - 9a =27$

$9(b - a) =27$

$(b - a) = 3 [==>Equation 2]$

Putting the two Equation's together ,we get:

a + b = 9

-a + b = 3

_______[By adding]

2b = 12

b = 6

Putting the value in the equation 1,we get:

a + 6 = 9

a = 3.

Hence ,a = 3and b = 6.

Therefore,the no. is 10(3) + 6 = 36...

Answer 2

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Question}}}}}}$

• Sum of two digits of a two digit number is 9 when we interchange the digit it is found that the resulting new number is greater than the original number by 27 what is the two digit number

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Question}}}}}}$

let the no. be 10x + y

x + y = 9 -----(i)

no. after interchange = 10y + x

10y + x - (10x + y) = 27

10y + x - 10x - y = 27

9y - 9x = 27

9( y - x) = 27

y - x = 27 /9

y - x = 3 ---------(ii)

adding eq (i) and (ii)

x + y + y - x = 9 + 3

2y = 12

y = 12 / 2

y = 6

• putting value of y in eq (i)

x + y = 9

x + 6 = 9

x = 9 - 6

x = 3

• Required no.

10x + y = 10 x 3 + 6 = 30 + 6 = 36

$\sf{\bold{\red{\boxed{\dag required \: no. = 36}}}}$

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