GATE 2020 EE GA Q.10: solution and answer

GATE 2020 · EEGA Q.10 · 2 marks · MCQ

The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was ______.

GATE 2020 EE GA question 10: Clustered vertical bar chart titled "Revenue and Expenditure (in million rupees) of four companies P, Q, R and S in… — Figure from the GATE 2020 EE paper. It is part of the question.

(A)
32.7
(B)
33.7
(C)
34.1
(D)
35.1

Answer and solution

ANSWER

Company Q's expenditure in 2014 was $\frac{45}{1.2 \times 1.1} = \frac{37.5}{1.1} \approx 34.1$ million rupees, which is option (C).

Official answer: CSource: Official answer key, GATE 2020 EE (IIT Delhi)

Read the chart. Only company Q's 2015 revenue matters here: its revenue bar stands at $45$ million rupees. The 2015 expenditure bar ( $35$ ) is a distractor, because the question asks about 2014.
Revenue in 2015 was 20% more than in 2014, so $R_{2015} = 1.2 R_{2014}$ . That gives $R_{2014} = \frac{45}{1.2} = 37.5 million rupees$ .
A profit of 10% on expenditure means profit $= 0.1 E_{2014}$ , so revenue $= E_{2014} + 0.1 E_{2014} = 1.1 E_{2014}$ .
Set $1.1 E_{2014} = 37.5$ . Then $E_{2014} = \frac{37.5}{1.1} = 34.09 \dots \approx 34.1 million rupees$ .
This value matches option (C).

KEY IDEA

Work backwards from the chart value in two steps. A 20% rise means dividing by $1.2$ to get the 2014 revenue. A 10% profit on expenditure means revenue $= 1.1 \times$ expenditure, so you then divide by $1.1$ . Together: $E_{2014} = \frac{45}{1.2 \times 1.1} = \frac{45}{1.32} \approx 34.1$ .

WATCH OUT FOR

There are three usual slips. (1) Taking 20% off the 2015 revenue ( $45 \times 0.8 = 36$ ) instead of dividing by $1.2$ . (2) Treating the profit as 10% of revenue, which gives $E = 0.9 \times 37.5 = 33.75$ , close to the distractor 33.7. (3) Using Q's 2015 expenditure bar ( $35$ ), which gives option (D) 35.1 or something near it. The 2015 expenditure is not needed at all.

From the GATE 2020 EE paper. Every question of this paper · Download the full paper · All 9 Data interpretation questions, with notes

GATE 2020 EE GA Q.10: solution and answer

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