Understanding the Percentage Profit Increase Question

The question asks us to find the percentage increase in the profit of Company X from the year 2014 to the year 2016. To calculate the percentage increase, we need to know the profit value in 2014 and the profit value in 2016. The formula for percentage increase is:

$\text{Percentage Increase} = \frac{\text{Profit in 2016} - \text{Profit in 2014}}{\text{Profit in 2014}} \times 100\%$

We need to determine which of the given statements, alone or together, provides enough information to calculate this percentage increase.

Analyzing Statement 1 for Data Sufficiency

Statement 1 says: "Company profit in 2014 was Rs. 1 lakh, which is 10% more than that m 2015."

• This statement gives us the profit in 2014: Profit in 2014 = Rs. 1 lakh.
• It also relates the profit in 2014 to the profit in 2015, but the profit in 2015 is not needed to answer the question about the increase from 2014 to 2016.
• This statement does not provide any information about the profit in 2016.

Since we do not have the profit in 2016 from Statement 1, we cannot calculate the percentage increase from 2014 to 2016 using only Statement 1. Therefore, Statement 1 alone is not sufficient.

Analyzing Statement 2 for Data Sufficiency

Statement 2 says: "Company profit in 2016 was Rs. 2 lakh, which was Rs. 1 lakh more than that in 2014."

• This statement gives us the profit in 2016: Profit in 2016 = Rs. 2 lakh.
• It also tells us that the profit in 2016 was Rs. 1 lakh more than the profit in 2014. We can write this relationship as:

Profit in 2016 = Profit in 2014 + Rs. 1 lakh

• Substituting the known value of Profit in 2016:

Rs. 2 lakh = Profit in 2014 + Rs. 1 lakh

• We can now find the Profit in 2014 from this equation:

Profit in 2014 = Rs. 2 lakh - Rs. 1 lakh = Rs. 1 lakh.

• So, Statement 2 provides both the Profit in 2014 (Rs. 1 lakh) and the Profit in 2016 (Rs. 2 lakh).

With both the Profit in 2014 and the Profit in 2016 known, we can calculate the percentage increase:

Percentage Increase = $\frac{\text{Rs. 2 lakh} - \text{Rs. 1 lakh}}{\text{Rs. 1 lakh}} \times 100\%$

Percentage Increase = $\frac{\text{Rs. 1 lakh}}{\text{Rs. 1 lakh}} \times 100\%$

Percentage Increase = $1 \times 100\% = 100\%$

Since we can calculate the percentage increase using only Statement 2, Statement 2 alone is sufficient.

Conclusion on Statement Sufficiency

Based on the analysis:

• Statement 1 alone is not sufficient because it does not give the profit in 2016.
• Statement 2 alone is sufficient because it provides enough information to find both the profit in 2014 and the profit in 2016.

Therefore, Statement 2 alone is sufficient, while Statement 1 alone is not sufficient to answer the question about the percentage increase in profit from 2014 to 2016.

Revision Table: Company Profit Data Sufficiency

Additional Information: Percentage Change Calculation

Percentage change is a fundamental concept used to show how much a quantity changes over time or between two points compared to the initial quantity. It can be an increase or a decrease.

• Formula for Percentage Increase:
  If a value increases from V_initial to V_final, the percentage increase is $\frac{\text{V}_{\text{final}} - \text{V}_{\text{initial}}}{\text{V}_{\text{initial}}} \times 100\%$.
• Formula for Percentage Decrease:
  If a value decreases from V_initial to V_final, the percentage decrease is $\frac{\text{V}_{\text{initial}} - \text{V}_{\text{final}}}{\text{V}_{\text{initial}}} \times 100\%$. (Note: The numerator is positive, representing the amount of decrease).
• Data Sufficiency Questions: These questions test your ability to determine if the provided data (in statements) is adequate to answer a specific question. You don't necessarily need to calculate the final answer, just determine if it *can* be calculated.

In this specific profit increase problem, Statement 2 provided both the initial (2014) and final (2016) profit figures, making it sufficient.