the sum of the digits of a 2-digit number is 8. the number obtained by interchanging the digits exceed the given number by 18.find the given numbers.
Answers
Answer:
the number is 35
Step-by-step explanation:
let the number be 10x+y
here y is units place
x is in ten's place
the sum of the digits of a 2-digit number is 8.
x+y=8 ----------(1)
the number obtained by interchanging the digits exceed the given number by 18.
interchanging the number 10y+x
10y+x-(10x+y)=18
9(y-x)=18
y-x=2 ---------(2)
by solving (1) and (2) we get,
y=5 and x=3
the number is 35
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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