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 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 \(0.22\times 20000=Rupees \;4400\). \[ \boxed{Rupees \;4400} \]

Answer 2

Since both increases are percentages of a running salary, their ratio can be found without ever solving for the original salary.

1. Rupees 2000: Checking the ratio \(2000:6600\approx0.303\), but the required ratio of second to third increase is \(2:3\approx0.667\), so this doesn't match.
2. Rupees 2200: Here \(2200:6600\approx0.333\), still not matching the required \(0.667\) ratio.
3. Rupees 4000: Here \(4000:6600\approx0.606\), close to but not exactly \(2/3\approx0.667\), so it is not the exact value.
4. Rupees 4400: Here \(4400:6600=2/3\) exactly, matching the required ratio.

The second increase is \(20\%\) of the salary after year 1, i.e. \(0.20\times1.10S=0.22S\), and the third increase is \(25\%\) of the salary after year 2, i.e. \(0.25\times1.32S=0.33S\). Their ratio is \(0.22S:0.33S=2:3\), so the second increase \(=\dfrac{2}{3}\times6600=4400\).

So the correct answer is Rupees 4400.