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18 votes
18 votes

A shaving set company sells $4$ different types of razors- Elegance, Smooth, Soft and Executive.

Elegance sells at $\text{Rs.} \ 48$, Smooth at $\text{Rs.} \ 63$, Soft at $\text{Rs.} \ 78$ and Executive at $\text{Rs.} \ 173$ per piece. The table below shows the numbers of each razor sold in each quarter of a year.

$$\begin{array}{|c|r|r|r|r|} \hline \textbf{Quarter/Product} & \textbf{Elegance} &\textbf{Smooth} &\textbf{Soft} & \textbf{Executive}\\\hline \text{Q1} & \text{27300} &\text{20009} &\text{17602} &\text{9999}\\\hline \text{Q2} & \text{25222} &\text{19392} & \text{18445}& \text{8942}\\\hline \text{Q3} & \text{28976} &\text{22429} & \text{19544} & \text{10234}\\\hline \text{Q4} &\text{21012} & \text{18229} & \text{16595} & \text{10109}\\\hline \end{array}$$

Which product contributes the greatest fraction to the revenue of the company in that year?

  1. Elegance
  2. Executive
  3. Smooth
  4. Soft
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5 Answers

Best answer
21 votes
21 votes

To calculate the revenue generated by each product in a year we need to first calculate total units of each category sold, and then multiply it with the cost per unit.

$$\overset{\textbf{Revenue generated by products}}{\begin{array}{|l|r|r|r|r|} \hline \textbf{} & \textbf{Total units sold} &\textbf{Price per unit} &\textbf{Total revenue} \\\hline \text{Elegance} & \text{102,510} &\text{48} &\text{4,920,480} \\\hline \text{Smooth} & \text{80,059} &\text{63} & \text{5,043,717}\\\hline \text{Soft} & \text{72,186} &\text{78} & \text{5,630,508} \\\hline \text{Executive} &\text{39,284} & \text{173} & \text{6,796,132} \\\hline \end{array}}$$

From the table above we can see that the max revenue is generated by Executive. 

Hence answer is B.

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15 votes
15 votes
b executive

We have to find the product $x$ which has $\max \left(\sum_{i=1}^4 n_{x_i} \times P_x \right)$, where $P_x$ is the selling price of $x$ and $n_{x_i}$ is the number of items of type $x$ sold in quarter $i$.
5 votes
5 votes
Let me give a piece of advice. See this is GATE exam. There's no point they would give these basic questions. Anyone can answer these. The trick here is how quickly we do. There's no point of rushing with the calculators, moreover with a virtual one, which would take even more time. Just apply common sense. Here, Executive ones are 4x, 3x and 2.5x costlier than Elegance, Smooth and Soft ones respectively. Just by looking at the table we can see that the units of Executives ain't that less in that ratio than the others. So it's obvious that Executives would produce maximum revenue.
1 votes
1 votes
Revenue from Elegance = (27300+25222+28976+21012) * Rs. 48 = Rs. 4920480 Revenue from Smooth = (20009+19392+22429+18229) * Rs. 63 = Rs. 5043717 Revenue from Soft = (17602+18445+19544+16595) * Rs. 78 = Rs. 5630508 Revenue from Executive = (9999+8942+10234+10109) * Rs. 173 = Rs. 6796132 Total Revenue = Rs. 22390837   Fraction of Revenue for Elegance = 0.219 Fraction of Revenue for Smooth = 0.225 Fraction of Revenue for Soft = 0.251 Fraction of Revenue for Executive = 0.303   Thus, B (Executive) is the correct answer.
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