Understanding the Equation
The equation given is 20p / 3 = 40p. To solve for p, we need to manipulate the equation step-by-step.
Step 1: Eliminate the Fraction
- Multiply both sides of the equation by 3 to remove the fraction:
- 3 * (20p / 3) = 3 * (40p)
- This simplifies to:
- 20p = 120p
Step 2: Rearranging the Equation
- Now, we need to isolate p. We can do this by moving all terms involving p to one side:
- 20p - 120p = 0
- This simplifies to:
- -100p = 0
Step 3: Solving for p
- Divide both sides by -100:
- p = 0 / -100
- Thus, we find:
- p = 0
Conclusion
The solution to the equation 20p / 3 = 40p is:
- p = 0
Key Takeaway
- Always isolate the variable by performing inverse operations.
- Verify the solution by substituting p back into the original equation. In this case, both sides will equal zero, confirming that p = 0 is correct.
This methodical approach is crucial in solving linear equations effectively, especially in competitive exams like UPSC.