Data Interpretation Discussion

**Common Information**

Answer the questions on the basis of the information given below.

The following pie charts give the values of the sales and expenses of five companies — $P, Q, R, S$ and $T$ — as a percentage of the total sales and expenses of these five companies put together.

\[\text{Profit = Sales - Expenses}\]

\[\text{Profit percentage} = \left(\dfrac{\text{Profit}}{\text{Sales}}\right)×100\]

No company made a loss.

Q. |
Which of the companies had the highest profit percentage? |

✔ A. |
$P$ |

✖ B. |
$Q$ |

✖ C. |
$R$ |

✖ D. |
$\text{Cannot be determined}$ |

**Solution:**

Option(**A**) is correct

If the total sales are $10x$. the sales of different companies are:

$P → 2x$, $Q → 2.5x$, $R →1.5x$, $S →1x$ and $T → 3x$

If the total expenses are $10y$. the expenses of different companies are:

$P →1y$, $Q →2y$, $R → 2.2y$, $S → 1.8y$, $T → 3y$

$\text{Profit = Sales - Expenses}$ and given that no company made a loss, though we can't say which company had the highest profit, using the ratio of (profit/sales) we can say that the profit percentage is highest for $\textbf{P}$.

**Alternative solution:**

Since,

$\text{Profit percentage} = \left(\dfrac{\text{Profit}}{\text{Sales}}\right)×100$

$= \left(\dfrac{\text{Sales - Expenses}}{\text{Sales}}\right)×100$

$=\left(1-\dfrac{\text{Expenses}}{\text{Sales}}\right)×100$

Profit percentage of the company is highest if its ratio of $\dfrac{\text{Expenses}}{\text{Sales}}$ is least.

This ratio is least for $\textbf{P}$.

**Shubham**

*()
*

Profit percentage = (S-E)/S {ignoring factor of 100}

= 1- (E/S)

Smaller the E/S , bigger the profit percentage.

P is the answer.