Question

The sum digits in a two digit number formed by two digits from 1 to 9 is 8. if 9 is added to number then both digits become equal. find the number.

Answer 1

The number is 35

Given :

• The sum digits in a two digit number formed by two digits from 1 to 9 is 8.

• When 9 is added to number then both digits become equal.

To find :

The number

Solution :

Step 1 of 2 :

Form the equation to find the number

Let the unit digit be y and tens digit be x

Then number = 10x + y

Since sum digits in a two digit number formed by two digits from 1 to 9 is 8

∴ x + y = 8

⇒ y = 8 - x - - - - - (1)

When 9 is added to number then the number becomes

= 10x + y + 9

= 10x + (8 - x) + 9

= 9x + 17

Step 2 of 2 :

Find the number

We now apply Hit and trial method to find the value of x so that both digits of 9x + 17 become equal

For x = 1

9x + 17 gives 26

In the number 26 two digits are not equal

For x = 2

9x + 17 gives 35

In the number 35 two digits are not equal

For x = 3

9x + 17 gives 44

In the number 44 two digits are equal

∴ The required value of x = 3

From Equation 1 we get

y = 8 - 3 = 5

So the required number

= 10x + y

= (10 × 3) + 5

= 30 + 5

= 35

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