Algebraic Equation Setup
Let the original number be represented by the variable $x$. The problem states that "one-third of a number is increased by 10, the result is 65". We can translate this into an algebraic equation:
$ \frac{x}{3} + 10 = 65 $
Solving for the Number
To find the original number ($x$), we first isolate the term with $x$ by subtracting 10 from both sides of the equation:
$ \frac{x}{3} = 65 - 10 $
$ \frac{x}{3} = 55 $
Next, we solve for $x$ by multiplying both sides by 3:
$ x = 55 \times 3 $
$ x = 165 $
So, the original number is 165.
Calculating the Sum of Digits
The question asks for the sum of the digits of the original number, which is 165. The digits are 1, 6, and 5.
Sum of digits = $1 + 6 + 5$
Sum of digits = $12$
Final Answer
The sum of the digits of the original number is 12.
Important Questions from Linear Equation in 1 Variable
The sum of three fractions A, B, and C, A > B > C, is \(\frac{121}{60}\) . When C is divided by B, the resulting fraction is \(\frac{9}{10}\) , which exceeds A by \(\frac{3}{20}\) . What is the difference between B and C?
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
If the measure of one angle of a right triangle is 30° more than the measure of the smallest angle, then the measure of the smallest angle is:
A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
The sum of three consecutive number is 126. Find the highest number?
