Question

The salary of a man increases by 10\% in the first year, then by 20\% in the second year and then by 25\% in the third year. If the last increase is equivalent to an increase of Rupees 6600, then what is the equivalent of the second increase?

• A. Rupees 2000
• B. Rupees 2200
• C. Rupees 4000
• D. Rupees 4400

Hint:

Successive percentage changes apply \emph{multiplicatively}. To find an increment in a later year, multiply the base \(S\) by the cumulative factor up to that year and the given percentage.

Answer 1

The Correct Option is D

Step 1: Let the initial yearly salary be \(S\).
After 1st year: \(1.10S\).
After 2nd year: \(1.10\times1.20S = 1.32S\). Step 2: Use the third (last) increase.
Third increase amount \(=25\%\) of the salary after the second year \(=0.25\times(1.32S)=0.33S\).
Given this equals \(Rupees \;6600\): \(0.33S=6600 \Rightarrow S=20000\). Step 3: Compute the second increase.
Second increase amount \(=20\%\) of the salary after the first year \(=0.20\times(1.10S)=0.22S\).
Hence \(0.22\times 20000=Rupees \;4400\). \[ \boxed{Rupees \;4400} \]