GATE CSE 2016 | Set 1 | GA | Question: 06

Question

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?

• A. Elegance
• B. Executive
• C. Smooth
• D. Soft

Comments

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.

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Without touching calculator i approximately summed up all the four revenues and the are 81k, 79k, 70k,37k, 64k 

now, we know multiplying a number n by k means increasing it by k times 

we have per unit price as 48, 63, 78, 173 

all the other values are less than 200 or say in between 45 and 80 times except 173, that means the multiplication with 173 will result in greatest number and answer is Executive

 

correct me if i am wrong

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I solved the question by long method of adding everything , I came here to see if someone got a more better smart approach didnt find any so i thought of this approach of calculating rough esitimates or approximations instead of full calculation and then multiplying by rates using calc 

Estimate Yearly Volumes (Rough Sums):

• Executive: $\approx 10\text{k} + 9\text{k} + 10\text{k} + 10\text{k} = \mathbf{39\text{k}}$

• Soft: $\approx 17.5\text{k} + 18.5\text{k} + 19.5\text{k} + 16.5\text{k} = \mathbf{72\text{k}}$

• Smooth: $\approx 20\text{k} + 19\text{k} + 22\text{k} + 18\text{k} = \mathbf{79\text{k}}$

• Elegance: $\approx 27\text{k} + 25\text{k} + 29\text{k} + 21\text{k} = \mathbf{102\text{k}}$ 

then 173 * 39 wins 

Answer 1

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.

Answer 2

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 $i$.

Comments

how do u calculated it?

Answer 3

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.

Comments

'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?

Please estimate once more.

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.

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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.

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Nice discussion going on bw pradip and chaudhary . smiley face emojis

Answer 4

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.

Comments

perfect

Answer 5

Answer: B.

Let the prices in order be p1, p2, p3 and p4. Likewise, let the numbers sold be n1, n2, n3 and n4.  

• p4: p3 > 2 and n3: n4 < 2 (in almost all quarters)
• p4: p2 = 3 (approx.) and n2: n4 = 2 (approx.)
• p4: p1 = 4 (approx.) and n1: n4 = 2.6-2.7

In all three cases, the ratio (p4*n4): (pi*ni) > 1 (i = 1, 2, 3). 

Of course, this is an observation based approach. The numbers for all quarters of any category are very close which makes this approach suitable.

Answer 6

After summation dont divide by sell 

there we have to multiply this camn be mistake by many student 

 

i did same so i got elegance as answer but actual ans is Executive generated more revenue 

Option B is answer