Question

the sum of a number of two digits and of the number formed by reversing the digits is 110 and the difference of the digits is 6 find the number

Answer 1

Hey there !!

Let the ten's digit of original number be x .

And, the unit's digit of the original number be y .

The original number = 10x + y .

Number obtained on reversing the digits = 10y + x .

Now, A/Q

⇒ ( 10x + y ) + ( 10y + x ) = 110 .

⇒ 11x + 11y = 110 .

⇒ 11( x + y ) = 110 .

⇒ x + y = 110/11 .

∵ x + y = 10...............(1) .

And,

∵ x - y = 6 .............(2) .

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

x + y = 10 .

x - y = 6 .

-   +    -

__________

⇒ 2y = 4 .

⇒ y = 4/2 .

∴ y = 2 .

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

∵ x + y = 10 .

⇒ x + 2 = 10 .

⇒ x = 10 - 2 .

∴ x = 8 .

Then, original number = 10x + y .

= 10 × 8 + 2 .

= 80 + 2 .

= 82 ..

Hence, the required number is 82 .

THANKS

#BeBrainly .

Answer 2

Here is your solution

Let,

The ten's digit of original number be x

The unit's digit of the original number be y

The original number= 10x + y

The Number obtained on reversing the digits = 10y + x

A/q

Add original numbers and reverse number.

So

=>( 10x + y )+( 10y + x )=110 .

=>11x + 11y = 110

=>11( x + y ) = 110

=>x + y = 110/11

x + y = 10...............(i)

x - y = 6 ..................(ii) (given)

On adding  equation (i) and (ii), we get

x + y + x - y= 10 +6

2x = 16

X=8

On putting the value of x in equation (i), we get

x + y = 10

8 + y = 10

Y = 10 - 8

y= 2

original number = 10x + y .

=>10 × 8 + 2

=>80 + 2

=>82

Hence,

The required number is 82

Hope it helps you