Question

The sum of two digits number and the number obtained by reversing the digits is 77 . If the differences of the digits of the number is 3 . Find the number

Answer 1

In the above Question , the following information is given -

The sum of two digits number and the number obtained by reversing the digits is 77 .

The differences of the digits of the number is 3 .

To find -

Find the required number .

Solution -

Here , the two following conditions is given -

Condition 1 -

The sum of two digits number and the number obtained by reversing the digits is 77 .

Condition 2 -

The differences of the digits of the number is 3 .

Now , let us assume that the required number is xy.

So , the reversed number becomes yx .

number xy -

=> 10x + y

Number yx -

=> 10y + x

The sum of two digits number and the number obtained by reversing the digits is 77 .

So ,

10x + y + x + 10 y = 77

=> 11x + 11y = 77

=> x + y = 7 ...... Equation 1 .

According to the second condition -

The differences of the digits of the number is 3 .

So ,

x - y = 3 ......... Equation 2

Adding equation 1 and equation 2

=> 2x = 10

=> x = 5

=> y = 7 .

Thus , the required number is 57 .

This is the answer .

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Answer 2

◘ Given ◘

• The sum of two digits number and the number obtained by reversing the digits is 77.

• The differences of the digits of the number is 3.

◘ To Find ◘

The original number.

◘ Solution ◘

Let the digit at ones place be x, and the digit at tens place be y.

• The original number is = 10y + x

• Number obtained by reversing it = 10x + y

A/q,

10x + y + 10y + x = 77

⟶ 11x + 11y = 77

⟶ 11(x + y) = 77

⟶ x + y = 7            . . . (i)

Now,

The differences of the digits of the number is 3.

________________

CASE - I

x - y = 3

⟶ x = 3 + y

Putting the value in equation (i) :

⟶ 3 + y + y = 7

⟶ 3 + 2y = 7

⟶ 2y = 4

⟶ y = 2

And,

x = 3 + 2

⟶ x = 5

The number is 10y + x = 20 + 5 = 25

________________

CASE - II

y - x = 3

⟶ y = 3 + x

Putting the value in equation (i) :

⟶ x + 3 + x = 7

⟶ 3 + 2x = 7

⟶ 2x = 4

⟶ x = 2

And,

y = 3 + 2

⟶ y = 5

The number is 10y + x = 25 + 2 = 52.

Therefore, the required number is 25 or 52.