Question

$\large{ \underline{ \underline{ \pmb{ \mathfrak{Question}}}}} :$


The sum of a two digit number and the number obtained by reversing the digits is 121. Find the number if it's unit digits is 5.​

Answer 1

★ Answer -

• The number is 65.

★ To find -

• The number.

★ Step-by-step explanation -

• In the question, it is given that the sum of a two digit number and the number obtained by reversing its digits is 121. We have to find the number.

As its unit digit is 5 -

• Let the tens digit be "x".

Then the number formed is -

$\tt \longrightarrow \: x \times 10 + 5 \times 1$

$\longrightarrow \: \tt 10x + 5$

Now, on reversing the digits of the number -

• The units digit becomes "x" while the tens digit becomes "5".

And the new number formed is -

$\longrightarrow \: \tt 5 \times 10 + x \times 1$

$\longrightarrow \: \tt50 + x$

According to the Question -

$\sf\implies (10x + 5) + (50 + x) = 121$

$\implies \sf 10x + 5 + 50 + x = 121$

$\implies \sf 11x + 55 = 121$

$\implies \sf 11x = 121 - 55$

$\implies \sf 11x = 66$

$\implies \sf x = \cancel\dfrac{66}{11}$

$\implies \underline{\boxed{\sf x = 6}} \: \bigstar$

Therefore -

• The tens digit is 6.

And the number is -

$\longmapsto \bf 10x + 5$

$\longmapsto \bf 10 \times 6 + 5$

$\longmapsto \bf 60 + 5$

$\longmapsto \bf 65$

Thus -

• The number is 65.

________________________________

Answer 2

Question

The sum of a two digit number and the number obtained by reversing the digits is 121. Find the number if it's unit digits is 5.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Required Answer

• ➡ 65

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Information mentioned in above question -

➡ The sum of a two digit number and the number obtained by reversing the digits is 121

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

What we have to Find out ;

• ➡ The required number which unit place digits is 5.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Consider :

• ➡ Assume that the Given units place digit be y and tens place digit be x

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Henceforth the two digit number

• ➡ 10 x + y

Number obtained by reversing the digits

• ➡ 10 y + x

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

According to the first condition given in question

• The sum of a two digit number and the number obtained by reversing the order of its digits is 121.

${\green{\implies}{\qquad{\sf{(10 \: x + y ) +( 10\: y + x ) = 121 }}}}$

${\green{\implies}{\qquad{\sf{10 \: x + y + 10\: y + x = 121 }}}}$

${\green{\implies}{\qquad{\sf{11 \: x \: + 11 \: y = 121 }}}}$

${\green{\implies}{\qquad{\sf{11 \: (x \: + y) = 121 }}}}$

${\green{\implies}{\qquad{\sf{\: x \: + y= \dfrac{121}{11} }}}}$

${\green{\implies}{\qquad{\sf{\: x \: + y= 11 \: \: ...(1) }}}}$

• Thus here we get eqution (1)

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

According to the second condition given in question

• Since the units place digit is 5

Therefore ➡ y = 5

Now by using substitution method :

• Place the value y = 5 in equation (1)

${\green{\implies}{\qquad{\sf{\: x \: + (5)= 11 \: \: ...(1) }}}}$

${\green{\implies}{\qquad{\sf{\: x \: = 11 - 5 }}}}$

${\green{\implies}{\qquad{\sf{\: x \: = 6 }}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

➡ Here we get the value of x and y so place the given values of x and y in 10 x + y

Henceforth by putting the values we get :

${\green{\implies}{\qquad{\sf{\: 10 \: \times (6) + (5)}}}}$

${\green{\implies}{\qquad{\sf{\: 60 + 5 = 65}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

• ❛❛ Therefore the required orginal number is 65♡ ❜❜

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Verification

• We know that the sum of a two digit number and the number obtained by reversing the digits is 121 so ,

${\green{\implies}{\qquad{\sf{(10 \: x + y ) +( 10\: y + x ) = 121 }}}}$

${\green{\implies}{\qquad{\sf{65+ 10 \times (5) + 6 = 121 }}}}$

${\green{\implies}{\qquad{\sf{65+ (50 + 6 )= 121 }}}}$

${\green{\implies}{\qquad{\sf{65+ 56= 121 }}}}$

${\green{\implies}{\qquad{\sf{121= 121 }}}}$

${\green{\implies}{\qquad{\sf{L.H.S = R.H.S}}}}$

Hence Verified

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

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