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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

Yes ,it is executive...
B because it is the costliest one and every quarter has increase in number, The other three has declined in some quarter.
These type of question is really time taken
In gate it is not wise to predict answer, but be 100% sure. But instead of doing the whole calculation, we can apply some shortcut. Manually, it is easy to do summation rather than multiplication. Hence from the given table directly do the addition for all 4 products ( who has done a lot of practice, it is very easy for then to add without actually writing all the numbers in paper, especially when the numbers are perfectly arranged ). Now you will see that the results are in decreasing order that is – 102,510; 80,059; 62,586; 39,284. Now, (price of Executive per piece / price of elegance per piece ) = 173/48 = 3.something. If we just do 39,284 * 3 = 117,852 > 102,510. so Executive produces highest revenue. I think this approach saves some time.

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.

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 $i$.

### 1 comment

how do u calculated it?
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.

in that way you will certainly secure -ve into your pocket.

it's good fortune that they didn't played any game and your rough prediction got hit.As i'm able to see we can't predict just by looking at the numbers here.
That's why all the faculties and the toppers say - read the question twice before answering.

If you go through the previous years aptitude questions you would find many like this.

In this particular questions it's way easy to estimate, not predict.

Anyway, it's my way of doing. But there surely are different approaches as well.

'reading question twice' , i consider this section in 'common sense'.You wait for someone's approval for this?

Certainly you are too smart to do estimation. Aren't you?

 Quarter product Elegance smooth soft Executive $Q_{1}$ 27500 20009 17602 9999 $Q_{2}$ 24590 37413 18445 2796 $Q_{3}$ 28976 22429 19560 4294 $Q_{4}$ 21012 20317 16784 15348

Per piece cost is 48,67,78,180 for elegance , smooth , soft , executive respectively.

People here are not stupid enough that they don't know how to estimate.Don't mind.I'm just careful that you don't get negative.

I'm really wondering from where you're coming up with words like predict and approval. Anyway, you're talking about being smart, as far as your replies are concerned, you don't seem to be smart enough to comprehend my answer to the question. So, if you feel like carrying on with this conversation, go ahead, alone. And thanks for your concern for my GATE. I'll keep your advice in mind if I'm ever going to appear for GATE, again.
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.

perfect