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 number.​

Answer 1

A n s w e r

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G i v e n

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• Sum of the digits of a 2 digit number is 8

• Number obtained by interchanging the digits exceeds the given number by 18

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F i n d

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• The given number

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S o l u t i o n

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Let the tens digit be "x"

Let the ones digit be "y"

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$\underline{\bold{\texttt{Original number :}}}$

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➠ 10x + y ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Reversed number :}}}$

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➠ 10y + x ⚊⚊⚊⚊ ⓶

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Given that , Sum of the digits of a 2 digit number is 8

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So,

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➜ x + y = 8 ⚊⚊⚊⚊ ⓷

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Also given that , Number obtained by interchanging the digits exceeds the given number by 18

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Equation ⓶ = Equation ⓵ + 18

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➜ 10y + x = 10x + y + 18

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➜ 10x - x + y - 10y = - 18

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➜ 9x - 9y = -18

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⟮ Dividing the above equation by 9 ⟯

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➜ x - y = -2 ⚊⚊⚊⚊ ⓸

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⟮ Adding equation ⓷ & ⓸ ⟯

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➜ x + y + x - y = 8 + (-2)

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➜ 2x = 6

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➜ $\sf x = \dfrac { 6 } { 2 }$

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➜ x = 3 ⚊⚊⚊⚊ ⓹

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• Hence the tens digit is 3

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⟮ Putting x = 3 from ⓹ to ⓷ ⟯

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➜ x + y = 8

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➜ 3 + y = 8

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➜ y = 8 - 3

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➜ y = 5 ⚊⚊⚊⚊ ⓺

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• Hence the ones digit be 5

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⟮ Putting x = 3 & y = 5 from ⓹ & ⓺ to ⓵ ⟯

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➜ 10x + y

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➜ 10(3) + 5

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➜ 30 + 5

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➨ 35

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• Hence the original given number is 35

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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

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