The line chart given below shows the percentage of net profit of company P and…
2021
The line chart given below shows the percentage of net profit of company P and company Q from 2014 to 2018. Formula : Net profit % = Income − Expenditure / Expenditure×100 Which of the following statement(s) is/are correct? I. If the income of company P in the year 2016 was Rs. 47250, then expenditure of the company in that year was Rs. 45500. II. If in 2016 the ratio of expenditure of company P to the expenditure of company Q is 4 : 5, then the ratio of income of company P to the income of company Q is 16 : 15.
- A.
Only I
- B.
Only II
- C.
Both I and II
- D.
Neither I nor II
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Correct answer: D
To determine the validity of the statements provided, we use the formula:
Net Profit % = ((Income - Expenditure) / Expenditure) * 100
This can be rearranged to: Income = Expenditure * (1 + (Net Profit % / 100)).
Statement I Evaluation
Data (2016): Company P's profit percentage = 5%.
Income: Rs. 47,250.
Calculation:
47,250 = Expenditure * (1 + 0.05)
47,250 = Expenditure * 1.05
Expenditure = 47,250 / 1.05 = 45,000.
Conclusion: Since the calculated expenditure is 45,000 and not 45,500, Statement I is incorrect.
Statement II Evaluation
Data (2016): Company P's profit % = 5%; Company Q's profit % = 15%.
Assumption: Ratio of Expenditure (P:Q) = 4:5. Let Expenditure of P = 4x, Expenditure of Q = 5x.
Calculate Income:
Income P = 4x * (1 + 0.05) = 4x * 1.05 = 4.2x
Income Q = 5x * (1 + 0.15) = 5x * 1.15 = 5.75x
Ratio of Income (P:Q):
4.2x : 5.75x = 420 : 575 = 84 : 115.
Conclusion: Since the calculated ratio is 84:115 and not 16:15, Statement II is incorrect.