Question

The sum of two digit no and number obtained by reversing the digit is 66.if the digits of the no differ by 2then find the number

Answer 1

Hi! Smile please, it suits your pretty face. Enjoy! :D

$\bold{\underline{\underline{\sf{\red{Given\::}}}}}$

• The sum of two digit no and number obtained by reversing the digit is 66.
• The digits of the number differ by 2.

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

• The original number.

$\bold{\underline{\underline{\sf{\red{ Solution\::}}}}}$

Let the digit at the tens place be x.

Let the digit at the units place be y.

Original Number : $\tt{10x\:+\:y}$

Reversed Number : $\tt{10y\:+\:x}$

$\bold{\sf{\underline{\underline{\green{As\:per\:the\:first\:given\:condition:}}}}}$

➦$\tt{10x\:+\:y\:+\:10y\:+\:x\:=\:66}$

➦$\tt{11x\:+\:11y\:=\:66}$

➦$\tt{\dfrac{11x}{11}\:+\:{\dfrac{11y}{11}\:=\:{\dfrac{66}{11}}}}$

➦$\tt{x+y=6\:\:\:\:\:(i)}$

$\bold{\sf{\underline{\underline{\green{As\:per\:the\:second\:given\:condition:}}}}}$

➦$\tt{x-y=2\:\:\:\:(ii)}$

Add equation (i) to (ii)

➦$\tt{x+y\:+\:x\:-y\:=\:6\:+\:2}$

➦ $\tt{2x\:=\:8}$

➦ $\tt{x\:=\:{\dfrac{8}{2}}}$

➦ $\tt{x=4}$

Substitute x = 4 in equation (i)

➦ $\tt{x+y=6}$

➦ $\tt{4+y=6}$

➦ $\tt{y=6-4}$

➦ $\tt{y=2}$

$\bold{\large{\boxed{\red{\mathcal{Ten's\:digit\:=\:x\:=\:4}}}}}$

$\bold{\large{\boxed{\purple{\mathcal{Unit's\:digit\:=\:y\:=\:2}}}}}$

$\bold{\large{\boxed{\blue{\mathcal{Original\:Number\:=\:10x\:+\:y\:=\:10\:\times\:4\:+\:2\:=\:40\:+\:2\:=\:42}}}}}$

#Shinchan_Lover ❤"

Answer 2

$\bold \red{The \: only \: way \: to \: learn \: Mathematics} \\ \bold \red{is \: to \: do \: mathematics :) }</p><p>$

We are here given with :

Sum of digits by reversing = 66

Digits differ by 2

We have to find :

The Original Number

Here,Goes the solution :D

Let the digit at unit's place be y and digit at ten's place be x

$\star \sf \: Original \: No = \bold \blue{10x + y}$

$\star \sf \: Interchanged \: No \:= \bold \blue{10y + x}$

According to the Question :

$\implies \sf \: 10x + y + 10y + x = 66$

$\implies \sf \: 11x + 11y = 66$

$\implies \sf \: 11(x + y) = 66$

$\implies \sf \: (x + y) = \cancel \dfrac{66}{11}$

$\sf \: x + y = \large\boxed{ \bold \blue{6}}.....(i)$

Again, According to the Question :

$\sf \: x - y = \large\boxed{ \bold \blue{2}}.....(ii)$

Now, add the equation (i) and equation (ii)

$\sf \green{x + y + x - y = 6 + 2}$

$\implies \sf \: 2x = 8$

$\implies \sf \: x = \cancel \dfrac{8}{2}$

$\sf \: x = \large\boxed{ \bold \pink{4}} \: Tens \: place \: digit$

Putting the value of x = 4 in equation i)

$\implies \sf \: x + y = 6$

$\implies \sf \: 4 + y = 6$

$\implies \sf \: y = 6 - 4$

$\sf \: y = \large\boxed{ \bold\pink{2}} \: Units \: place \: digit$

Hence,Original Number :

$\star \: \sf { \bold{\red{10 \times 4 + 2}}} \: = \large \: \boxed{ \bold{ \purple{42}}}$