Question

The sum of the digit of a 2 digit number is 11 . The number obtained by adding 4 to this number is 41 less than the reversed number. Find the original number

Answer 1

Given:-

• Sum of digits of 2 digit number = 11
• Numbers obtained by adding 4 is 41 less than reversed number.

To find:-

• Original number = ?

Solution :-

Let the digit at unit's place be m & digit at ten's place be n.

→ Original number = m + 10n

→ Reversed number = n + 10m

A/q,

→ m + n = 11

→ m = 11 - n ------ Equation (1)

Case 2 :

→ m + 10n + 4 = n + 10m - 41

→ m + 10n - n - 10m = -41 - 4

→ 9n - 9m = -45

→ 9(n - m) = -45

→ n - m = -45/9

→ n - m = -5

→ m - n = 5

→ m = n + 5 ------ Equation (2)

Comparing both equations :

→ 11 - n = n + 5

→ -n - n = 5 - 11

→ -2n = -6

→ n = -6/-2

→ n = 3

So, digit at ten's place = n = 3

Now,

→ Digit at unit's place = m

→ Digit at unit's place = n + 5

→ Digit at unit's place = 3 + 5

→ Digit at unit's place = 8

Now, two digit number:-

→ Two digit number = m + 10n

→ Two digit number = 8 + 10(3)

→ Two digit number = 8 + 30

→ Two digit number = 38

Therefore,

$\therefore\underline{\boxed{\textsf{Original two-digit number = {\textbf{38 }}}}}$

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The sum of the digit of a two digit number is 11. The number obtained by adding 4 to this number is 41 less than the reversed number.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The original number.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the one's digit be r

Let the ten's digit be m

$\underline{\sf{The\:Original\:number=10r+m}}}}\\\underline{\sf{The\:Reversed\:number=10m+r}}}}$

A/q

$\longrightarrow\sf{r+m=11}\\\\\longrightarrow\bf{r=11-m..............................(1)}$

&

$\longrightarrow\sf{10r+m+4=10m+r-41}\\\\\longrightarrow\sf{10r-r+m-10m=-41-4}\\\\\longrightarrow\sf{9r-9m=-45}\\\\\longrightarrow\sf{9(r-m)=-45}\\\\\longrightarrow\sf{r-m=\cancel{\dfrac{-45}{9} }}\\\\\longrightarrow\sf{r-m=-5}\\\\\longrightarrow\sf{11-m-m=-5\:\:\:\:[from(1)]}\\\\\longrightarrow\sf{11-2m=-5}\\\\\longrightarrow\sf{-2m=-5-11}\\\\\longrightarrow\sf{-2m=-16}\\\\\longrightarrow\sf{m=\cancel{\dfrac{-16}{-2} }}\\\\\longrightarrow\sf{\pink{m=8}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=11-8}\\\\\longrightarrow\sf{\pink{r=3}}$

Thus;

$\underbrace{\sf{The\:Original\:number\:=10r+m=10(3)+8=30+8=38.}}}}$