Question

A number consists of two digits whose sum is 5 when the digits are reversed the number becomes greater by 9 find the number

Answer 1

Step-by-step explanation:

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Answer 2

GIVEN :

• A number consists of two digits whose sum is 5. When the digits are reversed the number becomes greater by 9.

TO FIND :

• Number = ?

SOLUTION :

Let the digits in the tens be x and ones place be y.

Thus, the number is 10y + x

By reversing 10x + y

The sum of the digits of the number = 5

x + y = 5......(1)

And it is also given that, the new number so obtained after interchanging the digits is greater by 9 from the original number :

➨10x + y = 10y + x + 9

➨10x + y - 10y - x = 9

➨9x - 9y = 9

➨9(x - y) = 9

➨x - y = 9/9

➨x - y = 1....(2)

★ By adding equation (1) and (2) we get :

➨ (x + y) + (x - y) = 5 + 1

➨ x + y + x - y = 5 + 1

➨ 2x = 6

➨ x = 6/2

➨ x = 3

★ Putting x = 3 in the equation (1), we get :

➨ 3 + y = 5

➨ y = 5 - 3

➨ y = 2

Therefore, the required number is 10 × 2 + 3 = 23 .