Solving for the Original Number
Let the original number be represented by the variable $x$.
The problem states that one-third of the number, when increased by 55, results in 83. We can write this as an algebraic equation:
$ \frac{1}{3}x + 55 = 83 $
Calculating the Number
To find the value of $x$, we first isolate the term containing $x$:
- Subtract 55 from both sides of the equation: $ \frac{1}{3}x = 83 - 55 $ $ \frac{1}{3}x = 28 $
- Multiply both sides by 3 to solve for $x$: $ x = 28 \times 3 $ $ x = 84 $
The original number is 84.
Finding the Sum of Digits
The question asks for the sum of the digits of the original number (84).
- Sum of digits = 8 + 4
- Sum of digits = 12
The sum of the digits of the original number is 12.
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
