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. |
If the overall profit percentage of all the five companies put together was 50%. How many companies had a profit percentage greater than 60%? |

✖ A. |
0 |

✔ B. |
1 |

✖ C. |
2 |

✖ D. |
3 |

**Solution:**

Option(**B**) is correct

If overall profit percentage was 50%, it means that expenses are 50% of sales, It can be said that only company $P$ had a profit percentage greater than 60. While $Q$ had a profit percentage of exactly 60.

**Alternative solution:**

Let total sales = 100.

Then as overall profit percentage = 50%.

Total expenses will be 50.

Then the following will be the profit percentages of all the companies:

\begin{align*}

P &=\dfrac{20-5}{20}\\

&= 75\%\\

Q &=\dfrac{25-10}{25}\\

&= 60\%\\

R &=\dfrac{15-11}{15}\\

&= 26.67\%\\

S &=\dfrac{10-9}{10}\\

&= 10\%\\

T &=\dfrac{30-15}{30}\\

&=50\%

\end{align*}

Hence only $P$ has a profit percentage of above $60\%$

**Chhavi Sahni**

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**Chhavi Sahni**

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If your Sales are equal to 100 and Profit percentage is 50%, then the Expenses will not be equal to 50

In this case, take Expenses to be 100 and hence Sales are equal to 150

So, the profit percentages of both P and Q come out to be greater than 60%

Hey Chhavi,

I believe solution is correct.

If we go by your method, i.e. 'take Expenses to be 100 and hence Sales are equal to 150', then overall profit percentage is not equal to $50\%$ as mentioned in the question. Rather it is $75\% \left(=\dfrac{150\times 50}{100}\right)$

Profit percentage is calculated on SALES and not on EXPENSES.

Okay. I didn't see that you had mentioned a modified definition of Profit Percentage in the question.

By definition, 'Profit Percentage' is calculated on Expenses and 'Profit Margin' is calculated on Sales