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. ?

Answer 1

Answer:

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

⇒ y = 6

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

⇒ x = 8

The 10th digit if two digit number is 8.

The original number formed is 86.

On reversing the digits,

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

Answer 2

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

According to first condition ,

$x + y = 14 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ..........(1)$

According to the second condition ,

$10x + y = 10y + x + 18 \: \: \:$

$\longrightarrow \: 10x - x + y - 10y = 18$

$\longrightarrow \: 9x - 9y = 18$

$\longrightarrow \: x - y = 2 \: \: \: \: \: \: \: \: \: \: \: ........(2)$

Add Eq (1) and Eq (2) .

$\longrightarrow(x + y) + (x - y) = 14 + 2$

$\longrightarrow \: 2x = 16$

$\longrightarrow \underline{ \: x = 8}$

Put the value of x in Eq (1) .

$\longrightarrow \: 8 + y = 14$

$\longrightarrow \: y = 14 - 8$

$\longrightarrow \underline{\: y = 6}$

ORIGINAL NUMBER = 86

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