Question

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.​

Answer 1

Let

1st digit = x

2nd digit = x -6

(10x +(x -6)) + (10(x -6) +x) = 110

10x +x -6 +10x -60 +x = 110

22x = 110 +6 +60

22x = 176

x = 176/22

x = 8

1st digit = x = 8

2nd digit = x -6 = 8 -6 = 2

Your number: 82

Check: 82 + 28 = 110, 8 -2 = 6

Answer 2

Step-by-step explanation:

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

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.

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