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Question

When one-third of a number is increased by 25, the result is 100. Find the sum of the digits of the original number.

The correct answer is
9

Number Calculation and Digit Sum

Let the unknown number be represented by the variable '$x$'.

The problem statement translates to the following algebraic equation:

$ \frac{1}{3}x + 25 = 100 $

Solving the Equation

To find the value of the number '$x$', follow these steps:

  • Subtract 25 from both sides of the equation:

    $ \frac{1}{3}x = 100 - 25 $

    $ \frac{1}{3}x = 75 $

  • Multiply both sides by 3 to isolate '$x$':

    $ x = 75 \times 3 $

    $ x = 225 $

Calculating the Sum of Digits

The original number is 225.

To find the sum of its digits, add the individual digits together:

Sum = $ 2 + 2 + 5 $

Sum = $ 9 $

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Important Questions from Number System

  1. 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 ?

  2. If the sum S is divided by 8, what is the remainder ?  

  3. If the sum S is divided by 60, what is the remainder ?

  4. 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.

  5. How many composite numbers are there from 53 to 97 ?

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