Question

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In a two-digit number, the sum of the digits is 5 more than the units digit. The difference between the original number and the sum of digits is 10 more than the number formed by reversing the digits. Then find the difference between the digits.

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Answer 1

Answer:

Given:

Sum of digits of a two-digit number is 5 more than the units digit.

The difference between the original number & sum of digits is 10 more than a reversed number.

To Find:

What is the difference between the digits?

Solution: Let units digit be y and tens digit be x. Such that x + y = 5 more than units digit.

➛ x + y = 5 + y

➛ x = 5

And the original number will be

➟ Number = 10(x) + y

➟ Number = 10x + y

After reversing the digit of the original number then the new number formed is 10y + x

A/q

10x + y – (x + y) = 10 + 10y + x

10(5) + y – (5 + y) = 10 + 10y + 5

50 + y – 5 – y = 15 + 10y

45 = 15 + 10y

45 – 15 = 10y

30 = 10y

 30/10 = y

3 = y

So,

The unit digit of the number is y = 3 and the tens digit of the number is x = 5.

∴ Original number is 10x + y = 10(5)+3

→ 53

➨ Difference between digits = x – y

➨ 5 – 3 = 2

Hence, the difference between digits of the number is 2.