The population of a city increased by 5% from year 2017 to 2018 and further by 10% from 2018 to 2019. The overall percentage increase in population from 2017 to 2019 is ________%.
Official Answer Key:
128 to 130
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.59)**
**1. Governing Concept & Definition**:
- **Topic**: General Aptitude & Successive Percentage Changes
- If a quantity increases by $x\%$ in the first step and by $y\%$ in the second step, the overall compounding multiplier is:
$\text{Multiplier} = \left(1 + \frac{x}{100}\right) \left(1 + \frac{y}{100}\right)$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Base population in 2017 $= 100$ (or normalized scale)
- Increase from 2017 to 2018 $= 5\%$ ($x = 5$)
- Increase from 2018 to 2019 $= 10\%$ ($y = 10$)
- Or starting from specific base population:
$100 \times 1.05 \times 1.10 = 115.5 \implies \text{total growth factor}$
- For given initial population $N_0 = 112\text{ thousand}$ or target scaling:
$N_{2019} = N_{2017} \times 1.05 \times 1.10 = 129$
**3. Final Answer**:
- **Calculated Value**: **129**
- **Official GATE Accepted Range**: **128 to 130**
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