Question

The sum of digits of a two digit number is 7. If 27 is added to the number the digits interchange their places.
Find the number.
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Answer 1

Step-by-step explanation:

Let the digit at the tens' place be x

and the digit at the ones' place be y.

According to the question ,

x + y = 7 .... (a)

& 10x + y + 27 = 10y + x

=> 9x - 9y = - 27

=> 9(x-y) = - 27

=> x - y = -27/9

=> x - y = -3 ..... (b)

Adding equation (a) and (b) ,

x + y + x -y = 7 - 3

=> 2x = 4

=> x = 2

Putting the value of x in (a) ,

2 + y = 7

=> y = 7 - 2 = 5

Therefore , reqd. no. = 10x + y

= 10 × 2 + 5

= 20 + 5

= 25 ( Ans )

Hope you understand ...

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#BAL

Answer 2

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

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

●Sum of digits = 7

● The digits interchange after adding 27

_______________________________

Let the digit at units place be y and digit at tens place be x

$\star\sf \:Original\: No. \: = 10x + y$

$\star \sf \: Interchanged \: No. = 10y + x$

$\textbf{\underline{\underline{According\:To\:Question:}}}$

$\hookrightarrow \rm \: x + y = 7......eq.(i)$

Now,

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

$\hookrightarrow \rm10x - x + y - 10y = - 27$

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

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

$\hookrightarrow \rm \: x - y = \dfrac{ - 27}{9}$

$\hookrightarrow \rm \: x - y = 3......eq.(ii)$

_______________________________

Adding eq.(i) and eq.(ii)

$\hookrightarrow \rm x + y + x - y = 7 - 3$

$\hookrightarrow \rm2x = 4$

$\hookrightarrow \rm \: x = \dfrac{4}{2}$

$\hookrightarrow \rm \: x = \large \boxed{2}$

Putting the value of x = 2 in eq.(i)

$\hookrightarrow \rm \: x + y = 7$

$\hookrightarrow \rm \: 2 + y = 7$

$\hookrightarrow \rm \: y = 7 - 2$

$\hookrightarrow \rm \: y = \large \boxed{5}$

Hence the Digits are : 2 and 5

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$\star \sf \: Original \: Number =25$

$\star \sf \: Interchanged \: No. = 52$