Question

The digit of a two digit number differ by 2. If the digit are interchanged of the resulting number is added to the original number, we get 154. Find the number.​

Answer 1

The digit of a two digit number differs by 2.

Let the tens digit number be x and ones digit number be y.

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

Tens digit number - Ones digit number = 2

$\implies\:\sf{x-y\:=\:2}$

$\implies\:\sf{x\:=\:2+y} \gray{.........(1)}$

If the digit is interchanged of the resulting number is added to the original number, we get 154.

Assumed tens digit number is x and ones digit number is y.

Therefore, Original number = 10(tens digit number) + (ones digit number)

⇒ 10(x) + y

Interchanged number = 10(ones digit number) + (tens digit number)

⇒ 10(y) + x

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

Interchanged number + Original number = 154

$\implies\:\sf{10x+y+10y+x\:=\:154}$

$\implies\:\sf{11x+11y\:=\:154}$

Take 11 as common on both sides

$\implies\:\sf{11(x+y)\:=\:11(14)}$

11 throughout cancel

$\implies\:\sf{x+y\:=\:14}$

Now, Substitute the value of x from (eq 1)

$\implies\:\sf{2+y+y\:=\:14}$

$\implies\:\sf{2+2y\:=\:14}$

Take 2 as common on both sides

$\implies\:\sf{2(1+y)\:=\:2(7)}$

$\implies\:\sf{1+y\:=\:7}$

$\implies\:\sf{y\:=\:7-1}$

$\implies\:\sf{y\:=\:6}$

Substitute value of y in (eq 1)

$\implies\:\sf{x\:=\:2+6}$

$\implies\:\sf{x\:=\:8}$

We have to find the original number. From the above calculations, we have tens digit number (x) = 8 and ones digit number (y) = 6

Therefore,

Original number = 10(8) + 6 = 86

Answer 2

Given

A word problem

• In which a two digit no differ by 2
• when we interchanged the digit the new + original no be 154

To find

the no

Solution

Let the no in one's place be X and tens be y

Then

Y-x=2______(1)

According to the question

Original no = 10y+X

Interchanged no= 10x+y

Now adding original no and interchanged no

10y+X+10x+y=154

=>11y+11x=154

=>11(y+x)=154

=>y+X=14________(2)

From equation (1) and (2)

Y-x=2

y+X=14

_____

=>2y=16

y=8

putting the value of y in equation (1)

y-x=2

=>8-x=2

X=6

No is 10y+X=80+6=86

Hence,The no is 86