Question:hard

Directions:
Directions for the following 4 questions: The table below shows the annual Revenue and Expenditure (both in Rs. crore) of a company for five years. Profit in a year = Revenue - Expenditure. Study the data and answer the questions that follow. Year | Revenue | Expenditure 2019 | 120 | 80 2020 | 150 | 90 2021 | 180 | 120 2022 | 200 | 140 2023 | 250 | 175

In which year was the profit as a percentage of expenditure the highest?

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Rather than converting every ratio to a percentage, try comparing the profit-to-expenditure fractions two at a time using cross-multiplication to see which is bigger.
Updated On: Jul 8, 2026
  • 2020
  • 2019
  • 2021
  • 2023
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Instead of converting every Profit/Expenditure ratio into a decimal percentage, compare the fractions pairwise using cross-multiplication to find the largest without decimals.
Step 2: Profit for each year: 2019 $=120-80=40$; 2020 $=150-90=60$; 2021 $=180-120=60$; 2022 $=200-140=60$; 2023 $=250-175=75$.
Step 3: The Profit/Expenditure fractions are: 2019 $=\frac{40}{80}$, 2020 $=\frac{60}{90}$, 2021 $=\frac{60}{120}$, 2022 $=\frac{60}{140}$, 2023 $=\frac{75}{175}$.
Step 4: Compare 2020 ($\frac{60}{90}$) with 2019 ($\frac{40}{80}$) using cross-multiplication: $60\times80=4800$ versus $40\times90=3600$. Since $4800>3600$, $\frac{60}{90}>\frac{40}{80}$, so 2020 beats 2019.
Step 5: Compare 2020 with 2021: both have profit $60$, but 2020 has the smaller expenditure ($90$ vs $120$), so $\frac{60}{90}>\frac{60}{120}$; 2020 also beats 2022 for the same reason ($90<140$). Compare 2020 with 2023: $60\times175=10500$ versus $75\times90=6750$; since $10500>6750$, $\frac{60}{90}>\frac{75}{175}$. So 2020 has the highest profit-to-expenditure ratio among all five years. \[\boxed{2020}\]
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