the sum of the digits of two digit number is 8. The number obtained by interchanging the digit exceeds by the given number by 18. Find the given number.
Answers
Hey mate!!!!!
Here we can see that if the sum of two digit is 8 so they can be the following
1&7
2&6
3&5
4&4
And vice versa
Now we know that the difference of the numbers is 18 so let's see
71 - 17 = 54 ×
62-26 = 36 ×
53-35 = 18 ✓
44-44 = 00 ×
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 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__________________