Question

The sum of the digite of a 2-digit number is 8.
The number formed by interchanging the digits
exceeds the given number by 18. Find the given
numbers,​

Answer 1

Given

• The sum of the digits of a 2 digit number is 8.
• The number formed by interchanging the digits exceeds the given number by 18.

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To Find

• The given numbers.

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Solution

Let the one's digit number be 'x' and the ten's digit be '8 - x'

Original Number → 10 (Ten's Digit) + 1 (One's Digit)

$\sf \implies 10(8-x)+1(x)$

$\sf \implies 10(8) - 10(x) + x$

$\sf \implies80-10x+x$

$\sf \implies80-9x$

After Interchanging the digits,

One's digit → 8 - x

Ten's digit → x

New Number → 10 (Ten's Digit) + 1 (One's Digit)

$\sf \implies 10(x) + 1(8-x)$

$\sf \implies 10x+ 8 - x$

$\sf \implies 9x + 8$

So, as the question states, when the digits of the original numbers are interchanged the new number exceeds by 18.

New number - Original Number = 18

Let's solve the equation step-by-step

$\sf 9x + 8 -(80-9x) = 18$

Step 1: Simplify the equation.

$\sf \implies 9x + 8 -(80-9x) = 18$

$\sf \implies 9x + 8 - 80 + 9x = 18$

Step 2: Combine Like Terms.

$\sf \implies 9x + 8 - 80 + 9x = 18$

$\sf \implies (9x + 9x)+ (8 - 80) = 18$

$\sf \implies 18x-72=18$

Step 3: Add 72 to both sides of the equation.

$\sf \implies 18x-72+72=18+72$

$\sf \implies 18x=90$

Step 4: Divide 18 to both sides of the equation.

$\sf \implies \dfrac{18x}{18} = \dfrac{90}{18}$

$\sf \implies x = 5$

∴ x = 5

∴ One's digit ⇒ x = 5

∴ Ten's digit ⇒ 8 - x = 8 - 5 = 3

∴ Original number ⇒ 35

∴ New Number ⇒ 53

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Answer 2

Answer:

The original number is 35 and the new number is 53.

Step-by-step explanation:

Given :-

The sum of the digits of a 2-digit number is 8. The number formed by interchanging the digits exceeds the given number by 18.

To find :-

The given numbers.

Solution :-

Let the digit at one's place be x, then the digit at ten's place will be 8 - x.

Original number = 10(8-x) + x

• 80 - 10x + x
• 80 - 9x

After interchanging the digits, new number will be,

• 10x + 8 -x

• 9x + 8

ATP,

New number - Original number = 18

• 9x + 8 - (80 - 9x) = 18
• 18x - 72 = 18
• 18x = 18 + 72
• 18x = 90
• x = 90/18
• x = 5

∴ Digit at one's place (x) is 5

and digit at ten's place (8 -x) is 3.

∴ Original number is 35

and new number is 53.