Question

the sum of the digits of a number is 7.the difference between the number &the obtained by reversing its digits is 27.what is the number.​

Answer 1

Step-by-step explanation:

let the required number be:(10x+y)

now,

the new number obtained after reversing the digits is:(10y+x)

according to the question,

we have,

x+y=7 ------(1)

also,

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

=> 10x+y-10y-x=±27

=> 9x-9y=±27

=> x-y=±3 --------(2)

now , adding eq--(1) and(2),

we get,

=> 2x=7±3

=> 2x=10 or 4

=> x=5 or 2

thus,

if ,x=5, then y=2

and if x=2 ,then y=5

thus , we get two such numbers,:

25 or 52.

I hope it would help you out

thank you

Answer 2

Answer :

The number is 25 or 52.

Step-by-step explanation :

Given that :

• The sum of the digits of a number is 7.
• The difference between the number is 27.
• The obtained by reversing its digits is 27.

To Find :

The number.​

Solution :

$\bigstar}$ Consider as -

The digit at tens place as x.

The digit at ones place as y.

Now,

The number = 10x + y.

According to question,

x + y = 7

On reversing the digits, number becomes 10y + x

As Given :

⇒ (10y + x)-(10x + y)= 27

⇒ 9y - 9x = 27

⇒ y-x = 3

⇒ y+x = 7

Addition of  both equations,

⇒ 2y = 10

⇒ y = 5

⇒ x = 2

Hence the Required number is 25 or 52