Question

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

Answer 1

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Let the digits at ones place be x. Then,

the digits at tens place = (8-x)

Original number = 10(8-x) + x

= 80 - 10x + x

= 80 - 9x

On interchanging the digits

new number obtained = 10x + 8-x

= 9x + 8

According to question,

New number - Original number = 18

9x + 8 - (80-9x) = 18

=> 9x + 8 - 80 + 9x = 18

=> 18x - 72 = 18

=> 18x = 18 + 72

=> 18x = 90

=> x = 90/18

=> x = 5

Hence, the digits at ones place is 5.

The digits at tens place = (8-5) = 3.

So, the original number is 35 and the new number is 53.

Answer 2

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.

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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)⟹10(8−x)+1(x)

\sf \implies 10(8) - 10(x) + x⟹10(8)−10(x)+x

\sf \implies80-10x+x⟹80−10x+x

\sf \implies80-9x⟹80−9x

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)⟹10(x)+1(8−x)

\sf \implies 10x+ 8 - x⟹10x+8−x

\sf \implies 9x + 8⟹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) = 189x+8−(80−9x)=18

Step 1: Simplify the equation.

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

\sf \implies 9x + 8 - 80 + 9x = 18⟹9x+8−80+9x=18

Step 2: Combine Like Terms.

\sf \implies 9x + 8 - 80 + 9x = 18⟹9x+8−80+9x=18

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

\sf \implies 18x-72=18⟹18x−72=18

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

\sf \implies 18x-72+72=18+72⟹18x−72+72=18+72

\sf \implies 18x=90⟹18x=90

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

18x/18=90/18

∴ x = 5

∴ One's digit ⇒ x = 5

∴ Ten's digit ⇒ 8 - x = 8 - 5 = 3

∴ Original number ⇒ 35

∴ New Number ⇒ 53

___________hope it helps_____________