Question

The sum of the digits of a 2-digits number is 8 and the difference between the number and that formed by reversing the digits is 18, find the number.​

Answer 1

Given :-

• The sum of the digits of a 2-digits number is 8 and the difference between the number and that formed by reversing the digits is 18.

To find :-

• Required number

Solution :-

Let the tens digit be x then ones digit be y

Original number = 10x + y

• First condition

The sum of the digits of a 2-digits number is 8.

x + y = 8 ---(i)

• Second condition

The difference between the number and that formed by reversing the digits is 18.

10x + y - (10y + x) = 18

→ 10x + y - 10y - x = 18

→ 9x - 9y = 18

→ 9(x - y) = 18

→ x - y = 2 -----(ii)

Add both the equations

→ x + y + x - y = 8 + 2

→ 2x = 10

→ x = 10/2

→ x = 5

Putting the value of x in equation (ii)

→ x - y = 2

→ 5 - y = 2

→ y = 5 - 2

→ y = 3

Hence,

• Tens digit = x = 5

• Ones digit = y = 3

Therefore,

• Original number = 10x + y = 53

• Reversed number = 10y + x = 35

Answer 2

Given

• The sum of the digits of a 2-digits number is 8
• It formed by reversing the digits is 18

We Find

• Required Number in Question

Let's be x

• Let 10 number be x
• Ones digit also be y

So, original number is = 10x + y

We know that

The sum of two digit is 8

So, x + y = 8 [ First condition ]

The difference between the numbers and that formed by reversing the digits is 18.

= 10x + y - 10y - x = 18

= 9x - 9y = 18

= 9(x+y) = 18

= x - y = 18/9

= x - y = 2 [ Second Condition ]

According to the question

( We Adding Both equations )

= x + y + x - y = 8 + 2

= 2x = 10

= x = 10/2

= x = 5

Now we putting values

= x - y = 2

= 5 - y = 2

= y = 5 - 2

= y = 3

So, It is clear that

• X = 5
• Y = 3

So,

Original number is 10x + y = 53

Reversed number is 10y + x = 35

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