Question

The difference of digit of two digit number is 3. On reversing order of digit, the new number is diminshed by 27 than original number. Find the number​

Answer 1

$\bf{\huge{\underline{\boxed{\sf\purple{Answer:\:96}}}}}$

Given :

• Difference of  digit of two digit number is 3.
• On reversing order, new number is diminished by 27 than the original number.

To Find :

• The unknown number.

$\huge\underline\green{\tt Solution}$

Let the two - digit number be ' P ' and ' R '

Here,

unit digit = R

So, tens digit will be ' 10P '

Hence,

The given number is = 10P + R

( On reversing the digits )

= 10R - P

Also,

It is stated that the difference is 3 and the new number is diminished by 27 than the original number.

So,

10P + R - 10R - P = - 27

⇒ 9P - 9R = - 27

⇒ 9 ( P - R ) = -27

⇒ P - R = $\dfrac{27}{9}$

⇒ P - R = - 3

Now,

On reversing the digits,

R - P = 3

∵ Tens digit number will be more than the ones digit number.

So,

We can choose any number, like R = 9 and P = 6.

9 - 6 = 3 ( their difference is 3 ) Also,

Reverse of 96 = 69

So,

96 - 69 = 27 ( New number is diminished by 27 )

Therefore,

The number is 96.