Data Interpretation

Radar Chart

Medium

A large store has only three departments, Clothing, Produce, and Electronics. The following figure shows the percentages of revenue an cost from the three departments for the years 2016, $2017$ and 2018. The dotted lines depict percentage levels. So for example, in 2016, $50\%$ of store's revenue came from its Electronics department while $40 \%$ of its costs were incurred in the Produce department.

Figure for CAT 2019 DILR question 3 (Data Interpretation)

In this setup, Profit is computed as (Revenue - Cost) and Percentage Profit as Profit/Cost $\times 100 \%$ .

It is known that

The percentage profit for the store in $2016$ was $100 \%$ .
The store's revenue doubled from $2016$ to 2017, and its cost doubled from $2016$ to $2018$ .
There was no profit from the Electronics department in $2017$ .
In 2018, the revenue from the Clothing department was the same as the cost incurred in the Produce department.

What percentage of the total profits for the store in $2016$ was from the Electronics department?

Entered answer:

✅ Correct Answer: 70

Slide 1/8

Understanding the set :-

This is a Ternary Plots or Ternary Diagrams,

A ternary plot is a triangle-shaped chart used to show the proportions of three variables that always add up to a constant total (usually 100%).

In this set, we are looking at how a big store earns money and spends money across three departments:

Clothing, Produce (like fruits/vegetables), and Electronics.

For the years 2016, 2017, and 2018, you're given:

A triangle showing where the store's income (revenue) came from — which department made how much money.

Another triangle showing where the store's expenses (costs) went — which department cost how much to run.

The lines inside these triangles tell you the percentage of total income/cost that came from each department in each year.

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	20	30	50	30	40	30
2017	30	40	30	30	30	40
2018	40	40	20	20	50	30

This is a table we can make from the chart given in the set.

Clue 1 says,

The percentage profit for the store in 2016 was 100%.

=> If we consider the total cost in the year 2016 as 100,

then, the total revenue in 2016 must be $200$ .

Therefore, profit = 100% of total revenue = $100% of 200 = 100$

therefore, cost = $200 - 100 = 100$

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	30%	40 %	30%	30 %	30%	40 %
2018	40%	40%	20 %	20 %	50%	30 %

Now, we can find the revenue and cost of each department in the year 2016

Revenue in 2016 = 200 :-

Clothing - $200 * (20/100) = 40$

Produce - $200 * (30/100) = 60$

Electronics - $200 * (50/100) = 100$

Cost in 2016 = 100 "-

Clothing - $100 * (30/100) = 30$

Produce - $100 * (40/100) = 30$

Electronics - $100 * (30/100) = 30$

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	30%	40 %	30%	30 %	30%	40 %
2018	40%	40%	20 %	20 %	50%	30 %

Now, clue 2 says,

The store’s revenue doubled from 2016 to 2017, and its cost doubled from 2016 to 2018.

=> The store’s revenue doubled from 2016 to 2017,

the total revenue in the year 2016 = $200$ .

Thus, the total revenue in the year 2017 = $400$ .

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	120	160	120	30 %	30%	40 %
2018	40%	40%	20 %	20 %	50%	30 %

Now, we can find the revenue of each department in the year 2017.

for 2017 :

clothing - $400 * (30/100) = 120$

Produce - $400 * (40/100) = 160$

Electronics - $400 * (30/100) = 120$

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	120	160	120	90	90	120
2018	40%	40%	20 %	20 %	50%	30 %

Now, clue 3 says,

There was no profit from the Electronics department in 2017.

We know revenue of electronics department in 2017 = 120

Since, there was no profit

=> Cost of electronics = 120

=> In 2017,

Cost (electronis) = 40% = 120

=> total cost in 2017 = 300

From which we can find the cost of clothing and produce in 2017 as well,

which is 30% of 300.

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	120	160	120	90	90	120
2018	100	100	50	40	100	60

Clue 4 says,

In 2018, the revenue from the Clothing department was the same as the cost incurred in the Produce department.

Also, clue 2 says,

cost doubled from 2016 to 2018.

=> Cost in 2018 = $2 * 100 = 200$

=> cost of produce department = $50% of 200 = 100$

=> Revenue from clothing department = 40% = $100$

=> total revenue in 2018 = 250.

Year	Revenue - Clothing	Revenue - Produce	Revenue - Electronics	Cost - Clothing	Cost - Produce	Cost - Electronics
2016	40	60	100	30	40	30
2017	120	160	120	90	90	120
2018	100	100	50	40	100	60

Total profit in 2016 $=200-100=100$

Profit in $2016$ from Electronics dept $100 - 30 = 70$

Hence required $\%=\frac{70}{100} \times 100=70 \%$

Question 1

What was the percentage profit of the store in $2018$ ?

Question 2

What was the ratio of revenue generated from the Produce department in $2017$ to that in 2018?

Question 4

What was the approximate difference in profit percentages of the store in 2017 and 2018?

What percentage of the total profits for the store in 201620162016 was from the Electronics department?

Solution

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CAT Past Year Questions (Topic-Wise)

What percentage of the total profits for the store in $2016$ was from the Electronics department?