Question

3. The sum of the digits of a two digit number is 14. If the number formed by reversing the digits is less than the original number by 18 . find the original number.

​

Answer 1

Answer:

The original number is  86

Step-by-step explanation:

Let,

Units digit = x

Tens digit = 14 - x

Orignal Number :

⇒ 10 (14 - x) + x

⇒ 140x  - 10x + x

⇒ 140 - 9x

Digits are reversed:

⇒ 10x + x  14 - x

⇒ 10x - x + 14

⇒ 9x + 14

★ According to the question :

If the number formed by reversing the digits is less than the original number by 18 :

⇒ (140 -9x) - 18  =  (9x + 14)

⇒ 140 - 18 - 9x  =  9x + 14

⇒ 122 - 9x  =  9x + 14

⇒ -9x - 9x  =   14 - 122

⇒ - 18x  =  - 108

⇒  18x  =  108

⇒   x  =  108 / 18

⇒ x  =  6

Units digit = 6

Tens digit = 14 - x

⇒ 14 - x

⇒ 14 - 6

⇒  8

∴  The original number is  86

Answer 2

$\huge \purple A \purple N \purple s \purple W \purple e \purple \R:−$

Given:

Sum of the digits of a two digit number is 14.

Number formed by reversing digits is 36 less than original number.

To Find:

What is the original number ?

Solution: Let the unit and tens digit of number be y and x respectively. Therefore,

➟ x + y = 14 or

➟ x = (14 – y)........(1)

So original number will be :-

➯ Original number = (10x + y)

After reversing digits the number formed is:-

➯ Reversed number = (10y + x)

A/q

• Reversed number is 36 less than original number.

⟹ (10x + y) = (10y + x) + 36

⟹ 10x – x = 10y – y + 36

⟹ 9x = 9y + 36

⟹ 9(14 – y) = 9y + 36

⟹ 126 – 9y = 9y + 36

⟹ 126 – 36 = 9y + 9y

⟹ 90 = 18y

⟹ 90/18 = y

⟹ 5 = y

So,

➭ Unit digit of number is y = 5

➭ Tens digit = x = (14–y) = 14–5 = 9

Hence, The original number is

➫ (10x + y)

➫ 10(9) + 5 = 95