GATE BT 2020 | GA | Question: 10

Question

The profit shares of two companies $P$ and $Q$ are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company $P$ to the revenue of company $Q$, during $2013-2018$ is ________.

• A. $15 : 17$
• B. $16 : 17$
• C. $17 : 15$
• D. $17 : 16$

Answer 1

$$\text{Profit Percentage (\%)} = \frac{\text{Revenue} - \text{Investment}}{\text{Investment}} \times 100$$

$$\text{Revenue} = \text{Investment} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$$

$$\text{Total Revenue} = \sum \text{Revenue}_{\text{year}} = \sum \left[ I \times \left(1 + \frac{P_{\text{year}}}{100}\right) \right]$$

$$\text{Total Revenue} = I \times \sum \left(1 + \frac{P_{\text{year}}}{100}\right)$$

Since there are 6 years in total ($2013, 2014, 2015, 2016, 2017, 2018$):

$$\text{Total Revenue} = I \times \left( 6 + \frac{\sum P_{\text{year}}}{100} \right)$$

For Company P:

$$\sum P_P = 10 + 20 + 40 + 40 + 50 + 40 = 200\%$$

For Company Q:

$$\sum P_Q = 20 + 30 + 30 + 50 + 60 + 60 = 250\%$$

Total Revenue of Company P ($R_P$):

$$R_P = I \times \left( 6 + \frac{200}{100} \right) = I \times (6 + 2) = 8I$$

Total Revenue of Company Q ($R_Q$):

$$R_Q = I \times \left( 6 + \frac{250}{100} \right) = I \times (6 + 2.5) = 8.5I$$

$$\text{Ratio} = \frac{R_P}{R_Q} = \frac{8I}{8.5I} = \frac{8}{8.5} = = \frac{16}{17}$$