Math, asked by jdsingroha4, 7 months ago

Show the photo of the answer.The sum of a number of two digits and of the number formed by reversing the digits is 110 and the difference of the digits is 6.Find the number

Answers

Answered by Righi
2

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Answered by kush193874
4

Answer:

\sf \pink{\underline{\underline{\purple{Given :}}}}

The sum of a number of two digits and of the number formed by reversing the digits is 110.

And also, the difference of the digits is 6.

\sf \pink{\underline{\underline{\purple{To \: find :}}}}

The numbers.

\sf \pink{\underline{\underline{\purple{Solution :}}}}

It is told that sum of two digital number and after the reversing the digits the resultant no. is 110.

Let's assume that the no. are x and y respectively.

As it is told that :

Difference between them is 6

Therefore :

\bf \green{(x - y) = 6 ..........(i) }

Thereafter,

Considering :

The number x as ones digit and y as a tens digit.

Hence, no. formed is :

\red{ \leadsto \bf  {(10y + x) }}

After reversing the digits resultant no. will be :

\red{ \leadsto \bf  {(10x + y) }}

Now,

☯ \begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}

\bf  \implies \: (10y + x) + (10x + y) = 110 \\

\bf \implies 10x + x + 10y + y = 110 \\

\bf \implies 11x + 11y = 110 \\ \sf \:\:\:\: (taking \: \: common)

\bf \implies 11(x + y) = 110 \\

\bf \implies (x + y) =  \frac{ \cancel{110}}{ \cancel{11}}  \\

\bf  \green{ \therefore (x + y) = 10........(ii) }

Again,

Subtraction of both equations :

 \bf ( \cancel x - y) = 6 \\ \bf{ \underline{ -  ( \cancel x + y) =  - 10}} \\

\longmapsto\bf  \cancel - 2y =   \cancel- 4 \\

\bf \longmapsto 2y = 4 \\

\bf  \longmapsto \ y =  \frac{ \cancel 4}{ \cancel 2} \\

\bf \pink{  \longmapsto} \red{ \: y = 2}

Substituting the value of y in the equation ......(i) as follows :

 \bf \longmapsto (x - y) = 6 \\

 \bf \longmapsto (x - 2) = 6\\

 \bf \longmapsto x - 2 = 6\\

\bf \longmapsto x = 6 + 2\\

 \bf{ \pink{ \longmapsto }}  \:  \: \red{x = 8} \\

Thus,

x = 8 and y = 2

Therefore, the no. will be (10y + x)

➠ (10 × 8) + 2

➠ 80 + 2

➠ 82 ans.

or,

28 can be the answer.

\bold  \red \dag \bold{ \underline{ \boxed{ \red \odot \mid{ \bold {\bf{ \blue{Required  \: answer :  \green{ \sf 28 \: or \: 82  \gray\checkmark }}}}}}}} \bold  \red \dag

\sf \pink{\underline{\underline{\purple{Verification :}}}}

As it is told that their sum will 110.

i.e., the original no. + new no. = 110

Again,

\bf \longmapsto 82 + 28 = 110 \\

  \bf  \pink{\longmapsto} \red{ 110 = 110} \\

THUS,

L. H. S. = R. H. S.

  \bold\red \dag{ \underline{ \boxed { \bf{\green {Hence}, \:  \purple V \blue e \red r \pink i \gray f i \blue e \orange d }}}}\bold\red \dag

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