Question

the sum of digits of a two digit number is 3 if 9 is added to the number ,the digits are reversed ,find the number

by this
let the unit digit be X and ten's digit be x-3

fast​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

☆ Let digits at ones place be 'x'

☆ So, digits at tens place be 3 - x.

☆ So, number formed = 10(3 - x) + x = 30 - 10x + x = 30 - 9x

☆ Reverse number = 10 × x + 3 - x = 9x + 3

$\begin{gathered}\tt\red{According \: to \: statement}\end{gathered}$

$\tt \:  ⟼ \blue{30 - 9x + 9 = 9x + 3}$

$\tt \:  ⟼ \green{30 + 9 - 3 = 9x + 9x}$

$\tt \:  ⟼ \red{18x = 36}$

$\tt \:  ⟼ \: \blue{x \: = \: 2}$

$\begin{gathered}\begin{gathered}\bf number \: formed \: - \begin{cases} &\tt{30 - 9x = 30 - 9 \times 2 = 12} \end{cases}\end{gathered}\end{gathered}$

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Answer 2

Answer:

12

Step-by-step explanation:

Let the digit at unit's place be x and that at ten's place be y.

∴ x+y=3

∴ x=3-y         ------Equation - 1

So, the number will be : 10y+x.

If 9 is added to the number,

∴ 10y+x+9 = 10x+y  [∵ When 9 is added to number digits are reversed.]

∴ 9y +9 = 9x

∴ y + 1 = x  [∵ Taking 9 common]

∴ x = y + 1       -------Equation -2

Now, in both the equations LHS is same so RHS will also be equal.

∴ y+1 = 3-y

∴ 2y = 2

∴ y = 1

Substituting y=1 in 1st equation,

x= 3-1 = 2

Therefore, the number will be : 10(1) + 2 = 12

You can also check the answer by adding 9 to it, the result will 21 where both the digits get reversed/interchanged!

Hope this helps you out!

Mark it as brainliest if it did so:)