Data Interpretation Discussion

**Common Information**

The following bar graph shows the Income and Expenditures (in million US $) of five companies in the year 2001. The percent profit or loss of a company is given by:

[text{%Profit/Loss} = left(dfrac{text{Income – Expenditure}}{text{Expenditure}}right) × 100]

Q. |
If the income of Company $Q$ in 2001 was $10%$ more than its income in $2000$ and the Company had earned a profit of $20%$ in $2000$, then its expenditure in $2000$ (in million US $$$) was? |

✖ A. |
28.28 |

✔ B. |
30.30 |

✖ C. |
32.32 |

✖ D. |
34.34 |

**Solution:**

Option(**B**) is correct

Let the income of Company $Q$ in $2001 = x$ million US $\$$

Then, income of Company in $2001$:

$= \left(\dfrac{110}{100}\right) × x$ million US $\$$

$⇒ \left(\dfrac{110x}{100}\right)= 40$

$⇒ x = \left(\dfrac{400}{11}\right)$

i.e., income of Company $Q$ in $2000$:

$=\left(\dfrac{400}{11}\right)$ million US $\$$

Let the expenditure of Company $Q$ in $2000$ be $E$ million US $\$$

Then,

$20 = \dfrac{[400/11 - E]}{E} × 100$ [$\because$ % Profit = 20% ]

$⇒ 20 =\left[\dfrac{400}{11E} – 1\right] × 100$

$⇒ E = \left(\dfrac{400}{11}\right)× \left(\dfrac{100}{120}\right) = 30.30$

⇒ Expenditure of Company $Q$ in $2000 =30.30$ million US $\$$