Question

Ash Company reported sales of $\$400,000$ for year $1$,$\$450,000$ for year $2$, and $\$500,000$ for year $3$. Using year $1$ as the base year, what were the percentage increases for year $2$ and year $3$ compared to the base year?

• A. $80\%$ for year $2$ and $90\%$ for year $3$.
• B. $88\%$ for year $2$ and $80\%$ for year $3$.
• C. $88\%$ for year $2$ and $90\%$ for year $3$.
• D. $112.5\%$ for year $2$ and $125\%$for year $3$.
• E. $125\%$ for year $2$ and $112.5\%$ for year $3$.

Answer 1

The correct option is D

$112.5\%$ for year $2$ and $125\%$for year $3$.

Explanation for the correct option:

Find the percentage increase compared to the base year:

Given the sales is

$\$400,000$ for year $1$, which is base year

$\$450,000$ for year $2$, and

$\$500,000$ for year $3$

Here,

Percentage of increase in second year's sales compared to the first year's sale $=\frac{\text{total sales in second year}}{\text{total sales in first year}}\times 100$

$$\begin{gathered} =\frac{450000}{\text{400000}}\times 100 \\ =\frac{45}{40}\times 100 \\ =112.5\% \end{gathered}$$

Percentage of increase in third year's sales compared to the first year's sale $=\frac{\text{total sales in second year}}{\text{total sales in first year}}\times 100$

$$\begin{gathered} =\frac{500000}{\text{400000}}\times 100 \\ =\frac{5}{4}\times 100 \\ =125\% \end{gathered}$$

Therefore, the percentage increases for year $2$ is $112.5\%$ and for year $3$ is $125\%$ compared to the base (first) year .

Hence, option (D) is the correct answer.