Question

the sum of a digit of a two digit number is 6, if a digit are reversed, the new number will be 36 greater than the orignal number ,find the number

Answer 1

Let the two digit number be 10x +y

Given that the sum of its digits is 6

So, x + y = 6 (Equation 1)

Now the digits are reversed

So the number becomes 10y + x

Given that the new reversed number is 36 greater than the original number

So 10y + x = 10x + y + 36

10x - x = 10y - y - 36

9x - 9y = - 36

Taking 9 as common

9(x - y) = 9(-4)

x - y = - 4 (Equation 2)

Adding equation 1 and 2

x + y = 6

x - y = -4

2x = 2

x = 1

x + y = 6

x = 1 then y = 5

So, the number is 10(1) + 5 = 15.

Hope my answer helps you.  

Answer 2

Hey there !!

→ Let the ten's digit be x,

And, the one's digit be y.

A/Q,

⇒ x + y = 6..........(1).

→ Original number = 10x + y.

→ Number obtained by reversing the digit = 10y + x.

Now,

A/Q,

⇒ 10y + x = 10x + y + 36.

⇒ 10x - x + y - 10y = - 36.

⇒ 9x - 9y = -36.

⇒ 9( x - y ) = -36.

⇒ x - y = -4...........(2).

On substracting equation (1) and (2), we get

x + y = 6.

x - y = -4.

-  +    +

________

⇒ 2y = 10.

⇒ y = 10/2.

⇒ y = 5 .

Put the value of y in equation (1), we get

⇒ x + y = 6.

⇒ x + 5 = 6.

⇒ x = 6 - 5.

⇒ x = 1.

→ Original number = 10x + y.

= 10 × 1 + 5.

= 10 + 5.

= 15.

Hence, it is solved.

THANKS

#BeBrainly.