Question : In a factory, the production of cycles rose to 48,400 from 40,000 in 2 years. The rate of growth per annum is:
Option 1: 9%
Option 2: 8%
Option 3: 10.5%
Option 4: 10%
Correct Answer: 10%
Solution :
The production of cycles rose to 48400 from 40000 in 2 years.
Past production = 40000
Production after two years = 48400
Time = 2 years
Let $R$ be the rate of growth per annum.
According to the question,
Production after 2 years = past production $(1+\frac{\text{R}}{100})^2$
⇒ $48400 = 40000 (1+\frac{\text{R}}{100})^2$
⇒ $\frac{48400}{40000} = (1+\frac{\text{R}}{100})^2$
⇒ $\frac{484}{400} = (1+\frac{\text{R}}{100})^2$
⇒ $(\frac{22}{20})^2 = (1+\frac{\text{R}}{100})^2$
⇒ $\frac{22}{20} = 1+\frac{\text{R}}{100}$
⇒ $\frac{22}{20}-1 = \frac{\text{R}}{100}$
⇒ $\frac{2}{20} = \frac{\text{R}}{100}$
⇒ $R = 10$%
Hence, the correct answer is 10%.
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