Question

The following line graph gives the annual percent profit earned by a company during the period 1995 - 2000. If the income in 1998 was Rs. 264 crores, what was the expenditure in 1998?

• A. Rs. 104 crores
• B. Rs. 145 crores
• C. Rs. 160 crores
• D. Rs. 185 crores

Hint:

Remember the basic formula relating Profit Percentage, Income, and Expenditure: \[ \text{Profit Percentage} = \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \times 100 \] Rearranging this formula can help solve for any of the variables if the other two are known.

Answer 1

The Correct Option is C

Step 1: Determine the profit percentage in 1998 from the graph.
Looking at the line graph, the profit percentage in 1998 is 65\%. Step 2: Understand the relationship between Income, Expenditure, and Profit Percentage.
The profit percentage is calculated as:
$$\text{Profit Percentage} = \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \times 100$$ Step 3: Substitute the given values and solve for Expenditure.
We are given that the Income in 1998 was \( \rupee 264 \) crores, and the Profit Percentage was 65\%. Let the Expenditure in 1998 be \( E \) crores. Substituting these values into the formula: $$65 = \frac{264 - E}{E} \times 100$$ Now, we need to solve this equation for \( E \): $$\frac{65}{100} = \frac{264 - E}{E}$$ $$0.65 = \frac{264 - E}{E}$$ Multiply both sides by \( E \): $$0.65 E = 264 - E$$ Add \( E \) to both sides: $$0.65 E + E = 264$$ $$1.65 E = 264$$ Divide by 1.65: $$E = \frac{264}{1.65}$$ To simplify the calculation, we can multiply the numerator and denominator by 100: $$E = \frac{26400}{165}$$ Now, lets perform the division: $$E = 160$$ So, the expenditure in 1998 was \( \rupee 160 \) crores.