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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 ________.

1. $15 : 17$
2. $16 : 17$
3. $17 : 15$
4. $17 : 16$

edited

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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 $(B).$

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