The production of bottles rose to 26000 from 16000 in 2 years. Find the rate of growth per annum.
2 वर्षों में बोतलों का उत्पादन 16000 से बढ़कर 26000 हो गया। प्रतिवर्ष वृद्धि दर ज्ञात कीजिए।
Solution / समाधान:
Let the rate of growth per annum be r%.
Using the compound growth formula:
A = P(1 + r/100)^n
- A = Final amount (26000)
- P = Initial amount (16000)
- n = Number of years (2)
Substitute the values:
26000 = 16000 (1 + r/100)^2
Divide both sides by 16000:
(1 + r/100)^2 = 26000 / 16000 = 13 / 8
Take square root on both sides:
1 + r/100 = √(13/8) ≈ √1.625 ≈ 1.275
Subtract 1 from both sides:
r/100 = 1.275 − 1 = 0.275
Multiply both sides by 100:
r ≈ 27.5%
Final Answer: The rate of growth per annum is approximately 27.5%.
Quick Revision / Key Points
- Initial production (P) = 16000 bottles
- Final production (A) = 26000 bottles
- Time period (n) = 2 years
- Use compound growth formula: A = P(1 + r/100)^n
- Calculate r by isolating (1 + r/100) and taking square root
- Result: r ≈ 27.5% per annum
For more practice on percentage growth and related problems, you may refer to Percentage for SSC & Railway Exams: Formulas, Tricks, Examples & Practice Questions.