This problem involves calculating the income of three individuals, A, B, and C, based on given percentage relationships and a specific difference in income between two of them. We need to use the provided information to find the income of C.

Analyzing the Income Relationships

Let's break down the given information about the incomes of A, B, and C:

• The income of A is 30% less than the income of B.
• The income of B is 137.5% more than that of C.
• The income of A is Rs. 28500 less than that of B.

Translating Percentages to Equations

We can represent these relationships using mathematical equations. Let the incomes of A, B, and C be \(I_A\), \(I_B\), and \(I_C\) respectively.

• Income of A is 30% less than B: \(I_A = I_B - 30\% \text{ of } I_B\) \(I_A = I_B - 0.30 \times I_B\) \(I_A = (1 - 0.30) \times I_B\) \(I_A = 0.70 \times I_B\)
• Income of B is 137.5% more than C: \(I_B = I_C + 137.5\% \text{ of } I_C\) \(I_B = I_C + 1.375 \times I_C\) \(I_B = (1 + 1.375) \times I_C\) \(I_B = 2.375 \times I_C\)
• Income of A is Rs. 28500 less than B: \(I_B - I_A = 28500\)

Solving for Income B using the Difference

We know that \(I_B - I_A = 28500\) and \(I_A = 0.70 \times I_B\). We can substitute the expression for \(I_A\) into the difference equation:

Now, we can solve for \(I_B\):

So, the income of B is Rs. 95000.

Calculating Income C from Income B

We have the relationship \(I_B = 2.375 \times I_C\) and we now know \(I_B = 95000\). We can substitute the value of \(I_B\) into this equation:

To find \(I_C\), we need to divide 95000 by 2.375:

Let's convert 2.375 to a fraction to make the division easier. \(2.375 = 2 + 0.375\) \(0.375 = \frac{375}{1000} = \frac{3 \times 125}{8 \times 125} = \frac{3}{8}\) So, \(2.375 = 2 + \frac{3}{8} = \frac{16+3}{8} = \frac{19}{8}\).

Now substitute the fraction into the equation for \(I_C\):

Since \(95 \div 19 = 5\), it follows that \(95000 \div 19 = 5000\).

Therefore, the income of C is Rs. 40000.

Verification of Income Values

Let's check if these income values satisfy all the conditions:

• \(I_C = 40000\)
• \(I_B = 2.375 \times I_C = 2.375 \times 40000 = 95000\)
• \(I_A = 0.70 \times I_B = 0.70 \times 95000 = 66500\)

Check the difference between B and A:

This matches the given condition that the income of A is Rs. 28500 less than B. The calculated income for C is Rs. 40000.

Revision Table: Income Calculations

Here's a summary of the key values and calculations:

Additional Information: Percentage Increase and Decrease

Understanding how percentage increase and decrease work is crucial for solving such problems. Let's define these concepts:

• Percentage Decrease: If a value \(X\) is decreased by \(p\%\), the new value is \(X - (p/100) \times X = X(1 - p/100)\). In our problem, A's income is 30% less than B, so \(I_A = I_B(1 - 30/100) = I_B(1 - 0.30) = 0.70 I_B\).
• Percentage Increase: If a value \(X\) is increased by \(p\%\), the new value is \(X + (p/100) \times X = X(1 + p/100)\). In our problem, B's income is 137.5% more than C, so \(I_B = I_C(1 + 137.5/100) = I_C(1 + 1.375) = 2.375 I_C\). Note that a percentage increase of more than 100% means the new value is more than double the original value. A 100% increase doubles the value (original + original = 2x original). A 137.5% increase means the new value is the original value plus 137.5% of the original value, resulting in 237.5% of the original value.

These concepts are fundamental in solving problems involving percentages, ratios, and proportional relationships often found in quantitative aptitude sections of exams.