## The sum of two digit no. is 14. If the no. is formed by reversing the digit is less than the original no. by 18. Find the original no. ?

Question

The sum of two digit no. is 14. If the no. is formed by reversing the digit is less than the original no. by 18. Find the original no. ?

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1 month 2021-08-18T04:40:34+00:00 2 Answers 0 views 0

## The original number formed is 86.

Step-by-step explanation:

Let the two digits of two digit number be, 10th digit x and 1st digit y.

∴ x + y = 14

x = 14 – y   ⇒ (1)

The number formed is 10x + y

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

On reversing the digit the number will be 10y + x

⇒ 10y + x + 18 = (10x + y)

⇒ 10y + x = 10x + y – 18

⇒ 10y – y + x – 10x = – 18

⇒ 9y – 9x = -18 ⇒ (2)

Now substituting the value of x from (1) to (2)

⇒ 9y – 9 (14 – y) = – 18

⇒ 9y – 126 + 9y = – 18

⇒ 18y = 126 – 18

⇒ 18y = 108

⇒ y = 108/18

## Thus 1st digit if the number is 6

Substituting the derived value of y in (1) to derived value of x.

⇒ x = 14 – y

⇒x = 14 – 6

## The original number formed is 86.

On reversing the digits,

the number transform to 68, which is 18 less than original number

2. Let the ten’s place digit be x and one’s place digit be y .

According to first condition , According to the second condition ,    Add Eq (1) and Eq (2) .   Put the value of x in Eq (1) .   ## ORIGINAL NUMBER = 86

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