Let us assume both the companies $P$ and $Q$ invested $₹\;x.$
We know that, Revenue = Profit + Investment
Now, company $P$ revenue,
- $2013: 0.1x + x = 1.1x$
- $2014: 0.2x + x = 1.2x$
- $2015: 0.4x + x = 1.4x$
- $2016: 0.4x + x = 1.4x$
- $2017: 0.5x + x = 1.5x$
- $2018: 0.4x + x = 1.4x$
$\therefore$ Total revenue of company $P = 1.1x+1.2x+1.4x+1.4x + 1.5x+1.4x = 8.0x$
And company $Q$ revenue,
- $2013: 0.2x + x = 1.2x$
- $2014: 0.3x + x = 1.3x$
- $2015: 0.3x + x = 1.3x$
- $2016: 0.5x + x = 1.5x$
- $2017: 0.6x + x = 1.6x$
- $2018: 0.6x + x = 1.6x$
$\therefore$ Total revenue of company $Q = 1.2x+1.3x+1.3x+1.5x + 1.6x+1.6x = 8.5x$
Now, the ratio of the total revenue of company $P$ to the revenue of company $Q,$ during $2013−2018$ is $ = 8x: 8.5x = 16:17.$
$\textbf{Short Method:}$ Let us assume both the companies $P$ and $Q$ invested $₹\;100.$
Now, the total revenue of company $P = 110+ 120+140+140+150+140 = 800$
And, the total revenue of company $Q = 120+130+130+150+160+160 = 850$
$\therefore$ The required ratio $ = 800:850 = 80: 85 = 16:17.$
So, the correct answer is $(B).$