Question

the sum of the digits of a two digit number is 15. if the number formed by reversing the digits is less than the original number 27 . find the original number. ​

Answer 1

In the above Question , the following information is given -

The sum of the digits of a two digit number is 15 .

If the number formed by reversing the digits is less than the original number 27

To find -

Find the original number .

Solution -

Let the required number be ab .

The sum of the digits of a two digit number is 15 .

So , a + b = 15 .

Now ,

Original number - ab

Reversed Number - ba

Now ,

If the number formed by reversing the digits is less than the original number 27

ab = ba + 27

=> 10a + b = 10b + a + 27

=> 9a = 9b + 27

=> a = b + 3 .

Substituting this value -

a + b = 15

=> b + 3 + b = 15

=> 2b = 12

=> b = 6

=> a = 3 .

Thus , the required number is 36 .

This is the required answer.

_______________________

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 36

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The sum of the digits of a two digit number is 15

✭ If the number is reversed the new Number is 27 lesser than the original number

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Original Number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So now let the Original Number be 10x+y

Here,

≫ $\sf x+y= 15\qquad -eq(1)$

Now let the New Number be 10y+x

$\bullet\underline{\textsf{\: As Per the Question}}$

➝ $\sf 10x+y = 10y+x+27$

➝ $\sf 9x = 9y+27$

➝ $\sf x = y+3$

Substituting the value of eq(1)

»» $\sf x+y = 15$

»» $\sf y+3+y = 15$

»» $\sf 2y = 12$

»» $\sf \green{ y = 6}$

Therefore a = 3

Hence the Number is 36

$\rule{170}3$