Question

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

Answer 1

Answer:

Let the unit's place=x

Then the ten's place=15−x

∴ original number=10(15−x)+x=150−10x+x=150−9x

By reversing the digits, we get

New number=10x+(15−x)=10x+15−x=9x−15

According to the problem,

original number−New number=27

⇒150−9x−9x+15=27

⇒−18x+165=27

⇒−18x=27−165=−108

⇒x=

−18

−108

=6

Answer 2

Let

• 2 digits of a number be x and y.

So the number formed would be 10x + y

On reversing, the number would become 10y + x

Also in the question it is given that:

→ Sum of digits = 15

So, x + y = 15 ----- [Equation 1]

According to the question,

(10x + y) - (10y + x) = 27

⇒ 10x + y - 10y - x = 27

⇒ 9x - 9y = 27

⇒ 9 (x - y) = 27

⇒ x - y = 27 ÷ 9

⇒ x - y = 3 ------ [Equation 2]

Adding Equation 1 and Equation 2,

x + y = 15

{+} x - y = 3

2x = 18

⇒ x = 9

Substitute the value of X in Equation 1 to find out the value of y.

x - y = 3

⇒ 9 - y = 3

⇒ y = 6

We know that the original number is (10x + y)

10x + y

= 10(9) + 6

= 90 + 6

= 96

∴ Original number = 96