The salary of a person is increased by 10%, 20% and 25% successively in three consecutive years. Find the overall percentage increase in the salary at the end of the third year.
65%
To find the overall percentage increase in salary over three consecutive years with respective increases of 10%, 20%, and 25%, we can use the concept of successive percentage change.
The formula for successive percentage increase when two percentages \(x\%\) and \(y\%\) are applied successively is:
\(Overall\ Percentage\ Increase\ =\ x\ +\ y\ +\ \frac{x \cdot y}{100}\)
Let's apply this for each year:
- First Year: Increase = 10%
- Second Year: The effective increase after two successive increments of 10% and 20% can be calculated as:
- \(x = 10\%\), \(y = 20\%\)
- \(\text{Effective\ percentage\ increase} = 10 + 20 + \frac{10 \cdot 20}{100} = 32\%\)
- Third Year: Applying the 25% increase to the 32% effective increase from the previous two years:
- \(x = 32\%\), \(y = 25\%\)
- \(\text{Overall\ percentage\ increase} = 32 + 25 + \frac{32 \cdot 25}{100} = 65\%\)
Hence, the overall percentage increase in the salary at the end of the third year is 65%.
Therefore, the correct option is 65%.
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