Question

Sum of the digits of two digit number is 9. If 27 is added to the number the digits get reversed. Find the number.​

Answer 1

Answer:$Number=36$

Step-by-step explanation:

$x+y=9 ......1$

From 2nd

$10x+y+27=10y+x$

Solving

$x-y=-3 .........2$

Solving 1 and 2

$x+y=9$and $x-y=-3$

$x=3$and$y=6$

So,number=$10x+y=10(3)+(6)$

$=36$

Answer 2

$\mathfrak{\huge{\underline{Solution:}}}$

$\textbf{\huge{\underline{Given:}}}$

● Sum of two digits = 9

● After adding 27 the digits get reversed

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$\star$ Let the digit at units place be x and the digit at tens place be y.

$\rm \: x + y = 9.......eq.(i)$

[ If the digit of a two-digit number are x(ones) and y(tens),then the required number is 10y+x]

$\hookrightarrow \rm \:( 10x + y) + 27 = 10y + x$

$\hookrightarrow \: \rm \: 10x - x + y - 10y = - 27$

$\hookrightarrow \rm9x - 9y = - 27$

$\hookrightarrow \rm9(x - y) = - 27$

$\hookrightarrow \rm 9x - 9y = - 27.......eq.(ii)$

Multiplying 9 to the equation(i) on both sides.

$\hookrightarrow \rm \: 9(x + y) = 9(27)$

$\hookrightarrow \rm \: 9x + 9y =81........(eq.iii)$

Adding eq.(ii) and eq.(iii)

$\hookrightarrow \rm \: 9x- 9y + 9x + 9x = 81 - 27$

$\hookrightarrow \rm18x = 54$

$\hookrightarrow \rm \: x = \dfrac{54}{18}$

$\hookrightarrow \rm \: x = \large \boxed{3}$

Putting the value of x = 3 in eq.(i)

$\hookrightarrow \rm \: x + y = 9$

$\hookrightarrow \rm3 + y = 9$

$\hookrightarrow \rm \: y = 9 - 3$

$\hookrightarrow \rm y = \large \boxed{6}$

Hence,The number is 36