Question

The sum of two digit number is 11. If 63 is added to the number the digit get reversed. Find the number.




explain me​

Answer 1

✬ Number = 29 ✬

Step-by-step explanation:

Given:

• The sum of two digits of a number is 11.
• After adding 63 to number the digit of number get reversed.

To Find:

• What is the number ?

Solution: Let the unit and tens digit of number be y and x respectively. Therefore,

➟ x + y = 11 or x = 11 – y........(1)

➟ Number will be (10x + y)

• When we reverse the dight then the new number or reversed number formed will be •

➟ Reversed number = (10y + x)

A/q

• After adding 63 to the original number the digits gets reversed.

$\implies{\rm }$ (10x + y ) + 63 = (10y + x)

$\implies{\rm }$ 10(11 – y) + y + 63 = 10y – 11 – y

$\implies{\rm }$ 110 – 10y + y + 63 = 10y – 11 – y

$\implies{\rm }$ 173 – 9y = 9y + 11

$\implies{\rm }$ 173 – 11 = 9y + 9y

$\implies{\rm }$ 162 = 18y

$\implies{\rm }$ 162/18 = y

$\implies{\rm }$ 9 = y

Hence,

➮ Unit digit of number is y = 9

➮ Tens digit of number is x

=> (11 – y) = 11 –9 = 2

Therefore, the number will be (10x + y)

➨ 10(2) + 9 = 20 + 9 = 29

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• The sum of the digits of two digit number is 11

$\:\:$

• When 63 is added to the number the digit get reversed

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The number.

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the ones digit be 'y'

Let the tens digit be 'x'

$\:\:$

$\underline{\bold{\texttt{Original number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10x + y$

$\:\:$

$\underline{\bold{\texttt{Reversed number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10y + x$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

⇛ x + y = 11

$\:\:$

⇛ x = 11 – y --------(1)

$\:\:$

Also,

$\:\:$

After adding 63 to the original number the digits gets reversed.

$\:\:$

⇛ (10x + y ) + 63 = (10y + x)----------(2)

$\:\:$

$\underline{\bold{\texttt{Putting x = 11 - y in (2)}}}$

$\:\:$

⇛ 10(11 – y) + y + 63 = 10y + 11 – y

$\:\:$

⇛ 110 – 10y + y + 63 = 10y + 11 – y

$\:\:$

⇛ 173 – 9y = 9y + 11

$\:\:$

⇛ 173 – 11 = 9y + 9y

$\:\:$

⇛ 162 = 18y

$\:\:$

⇛ $\rm y = \dfrac { 162 } { 18 }$

$\:\:$

$\bf \dashrightarrow y = 9$

$\:\:$

Hence,

$\:\:$

• One's digit is y = 9

$\:\:$

• Tens digit of number is x

$\:\:$

⇛ (11 – y) = 11 –9 = 2

$\:\:$

$\underline{\bold{\texttt{Original number -}}}$

$\:\:$

⇛ (10x + y)

$\:\:$

⇛ 10(2) + 9 = 20 + 9

$\:\:$

$\purple\longrightarrow$ $\bf 29$

$\rule{200}5$