Question

58. 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​

Answer 1

$\large\bf\underline{Given:-}$

• Sum of digits is 5 more than the unit's digit

• The difference between the original number and the sum of digits is 10 more than the number formed by reversing the digits.

$\large\bf\underline {To \: find:-}$

• Difference between the digits.

$\huge\bf\underline{Solution:-}$

➺ Let the ten's place digit be x

➺ Let the unit's place digit be y.

• Then ,The number = 10x + y

Sum of digits = x + y = 5 + y

⠀⠀⠀⠀⠀⠀⠀⠀➸ x = 5 +y - y

⠀⠀⠀⠀⠀⠀⠀⠀➸ x = 5 ........(i)

So, ten's place digit = 5

After reversing the digits :-

• Number formed = 10y + x
• Original number = 10x + y

$\large \underbrace{ \star \bf \: According \: to \: question}$

The difference between the original number and the sum of digits is 10 more than the number formed by reversing the digits.

➸ (10x + y) - (y + 5) = (10y + x) + 10

➸ 10x + y - y - 5 = 10y + x + 10

➸ 10x -5 = 10y + x + 10...........(ii)

putting value of x = 5 from (i) in eq. (ii)

➸ 10 × 5 -5 = 10y + 5 +10

➸ 50 -5 = 10y + 15

➸ 45 = 10y +15

➸ 10y = 45 -15

➸ 10y = 30

➸ y = 3

• So, x = 5 and y = 3
• Original Number = 53

Difference between the digits = 5-3 = 2

★ Difference between the digits = 2

Answer 2

✬ Difference = 2 ✬

Step-by-step explanation:

Given:

• Sum of digits of a two digit number is 5 more than units digit.
• The difference between original number & sum of digits is 10 more than 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 original number then the new number formed is 10y + x

A/q

$\implies{\rm }$ 10x + y – (x + y) = 10 + 10y + x

$\implies{\rm }$ 10(5) + y – (5 + y) = 10 + 10y + 5

$\implies{\rm }$ 50 + y – 5 – y = 15 + 10y

$\implies{\rm }$ 45 = 15 + 10y

$\implies{\rm }$ 45 – 15 = 10y

$\implies{\rm }$ 30 = 10y

$\implies{\rm }$ 30/10 = y

$\implies{\rm }$ 3 = y

So,

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

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

→ 53

➨ Difference between digits = x – y

➨ 5 – 3 = 2

Hence, difference between digits of number is 2.