The table below presents the percentage profit earned by two companies A and B during the period 2013 to 2018. Based on the data given in the table, answer five questions that follow Yearwise percentage (%) profit [Where profit % = $\frac{Income − Expenditure}{Expenditure} × 100]$Year % Profit Earned A B 2013 20 % 35 % 2014 32 % 30 % 2015 40 % 50 % 2016 25 % 40 % 2017 30 % 30 % 2018 15 % 40 %
If the expenditure of company A in the year 2013 and company B in the year 2018 are the same, and the income of company B in the year 2018 is ₹ 77 lakhs, then what is the income of company A in the year 2013?
₹ 66 lakhs
To find the income of Company A in 2013, we need to use the information provided regarding the percentage profit and the relationship between income and expenditure.
We are given that:
- The expenditure of Company A in 2013 is equal to the expenditure of Company B in 2018.
- The income of Company B in 2018 is ₹ 77 lakhs.
The formula for percentage profit is given by:
\(% \text{ Profit} = \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \times 100\)
Applying the formula for Company B in 2018:
Let \(E_B\) be the expenditure of Company B in 2018. Then:
\(40 = \frac{77 - E_B}{E_B} \times 100\)
Solve the equation for \(E_B\):
\(\begin{align*} 40 & = \frac{77 - E_B}{E_B} \times 100 \\ 0.40 E_B & = 77 - E_B \\ 1.40 E_B & = 77 \\ E_B & = \frac{77}{1.40} \\ E_B & = 55 \, \text{lakhs} \end{align*}\)
Therefore, the expenditure for Company A in 2013 is also ₹ 55 lakhs.
Now, use the percentage profit formula for Company A in 2013 with the expenditure we just found:
\(20 = \frac{\text{Income}_A - 55}{55} \times 100\)
Let \(I_A\) be the income for Company A in 2013. Solve for \(I_A\):
\(\begin{align*} 20 & = \frac{I_A - 55}{55} \times 100 \\ 0.20 \times 55 & = I_A - 55 \\ 11 + 55 & = I_A \\ I_A & = 66 \, \text{lakhs} \end{align*}\)
Thus, the income of Company A in 2013 is ₹ 66 lakhs.
Therefore, the correct answer is: ₹ 66 lakhs.
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