Telephone Company Expenditure Calculation for 2018

Understanding the Problem

The question asks us to find the expenditure of a telephone company in the year 2018. We are given the income for 2018 and the profit percentage earned during that year. The profit percentage is defined as the difference between income and expenditure, divided by the expenditure, multiplied by 100.

Data Provided

• Year: 2018
• Income in 2018: Rs. 330 crores
• Profit Percentage in 2018: 65%

Formula for Profit Percentage

The formula given is:

Profit Percentage = $ \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \times 100 $

Let's denote Profit Percentage as $ P $, Income as $ I $, and Expenditure as $ E $.

So, the formula becomes:

$ P = \frac{I - E}{E} \times 100 $

Step-by-Step Solution

1. Rearrange the formula to solve for Expenditure ($E$):

   First, divide both sides by 100:

   $ \frac{P}{100} = \frac{I - E}{E} $

   Multiply both sides by $E$:

   $ \frac{P}{100} \times E = I - E $

   Add $E$ to both sides to gather all terms involving $E$:

   $ \frac{P}{100} \times E + E = I $

   Factor out $E$:

   $ E \left( \frac{P}{100} + 1 \right) = I $

   Simplify the term in the parenthesis:

   $ E \left( \frac{P + 100}{100} \right) = I $

   Finally, isolate $E$ by multiplying both sides by $ \frac{100}{P + 100} $:

   $ E = I \times \frac{100}{P + 100} $

   Alternatively, $ E = \frac{I \times 100}{P + 100} $

2. Substitute the given values for 2018 into the rearranged formula:

   Income ($I$) = 330 crores

   Profit Percentage ($P$) = 65%

   $ E = \frac{330 \times 100}{65 + 100} $

3. Calculate the Expenditure ($E$):

   $ E = \frac{33000}{165} $

   Performing the division:

   $ E = 200 $

Therefore, the expenditure of the telephone company in 2018 was Rs. 200 crores.

Table of Annual Profit Percentages (2015-2020)

This table shows the profit percentages for the relevant period, confirming the 65% profit for 2018 used in our calculation.