The following table shows the income, expenditure and profit percentage of a…
2023
The following table shows the income, expenditure and profit percentage of a company for six years from 2017 to 2022. Income and expenditure figures are in Rs. million and the percentage increase in profit percent in year 2022 in comparison to previous year is \(33\frac{1}{3}\%\). Based on the data in the table, answer the questions that follow.
Year-wise details of Income, Expenditure and Profit of a company
Year | Income (in Rs. million) | Expenditure (in Rs. million) | Profit% |
|---|---|---|---|
2017 | 103.824 | - | 12% |
2018 | - | 83.8 | 25% |
2019 | 95.76 | 84 | - |
2020 | 113.28 | - | 20% |
2021 | 133.1 | 110 | - |
2022 | 121.6 | - | - |
Note: Some values are missing in the table (marked as '-') that you are expected to calculate if required.
If the expenditure was increased by 20% in the year 2017 in comparison to the year 2016 and profit percentage in 2016 was 25% less than the profit percentage in 2017, then what is the income of the company in 2016? (in Rs. million)
Answer: D. 84.2025 — CONCEPTProfit percentage is measured on expenditure: Income = Expenditure × (1 + profit rate/100). A percentage decrease in a rate is applied…
- A.
83.2020
- B.
85.6211
- C.
81.2430
- D.
84.2025
Attempted by 2 students.
Show answer & explanation
Correct answer: D
CONCEPT
Profit percentage is measured on expenditure: Income = Expenditure × (1 + profit rate/100).
A percentage decrease in a rate is applied multiplicatively, and a 20% rise means the later expenditure is 1.20 times the earlier expenditure.
APPLICATION
Use the 2017 profit rate: 103.824 = Expenditure in 2017 × 1.12, so Expenditure in 2017 = 103.824 ÷ 1.12 = 92.7 million.
The 2017 expenditure is 20% above the 2016 expenditure. Therefore, Expenditure in 2016 = 92.7 ÷ 1.20 = 77.25 million.
The 2016 profit percentage is 25% less than 12%. Thus, the 2016 profit rate = 12% × (1 − 0.25) = 9%.
Income in 2016 = 77.25 × 1.09 = 84.2025 million.
CROSS-CHECK
The profit is 84.2025 − 77.25 = 6.9525 million, and 6.9525 ÷ 77.25 = 9%. Also, 77.25 × 1.20 = 92.7 and 92.7 × 1.12 = 103.824, so both given percentage relations are recovered.
Therefore, the required income is Rs. 84.2025 million.