Question

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee.

The overhead is 20% of the consulting fee if the fee is up to ₹5,00,000.
For higher fees, the overhead is ₹1,00,000 plus 10% of the amount by which the fee exceeds ₹5,00,000.
The government charges a Goods and Services Tax (GST) of 18% on the total amount (i.e., the consulting fee plus the overhead).
An employee of the organization charges this entire amount — that is, the consulting fee, overhead, and tax — to the client.

If the client cannot pay more than ₹10,00,000, what is the maximum consulting fee that the employee can charge?

• A. \rupee 7,01,438
• B. \rupee 7,24,961
• C. \rupee 7,51,232
• D. \rupee 7,75,784

Hint:

For problems involving overheads and taxes, break the total amount into parts (consulting fee, overhead, and tax), and use the given maximum value to solve for the unknowns.

Answer 1

The Correct Option is B

Let the maximum consulting fee be \( x \).

The overhead is calculated as:
For \( x \leq ₹5,00,000 \), overhead = \( 0.20x \).
For \( x > ₹5,00,000 \), overhead = ₹1,00,000 + \( 0.10(x - 5,00,000) \).

Also, the GST is 18% on the total amount (consulting fee + overhead). The client can pay a maximum of ₹10,00,000.

Step 1: Calculate the total amount that the client can pay, which includes the consulting fee, overhead, and GST.
The total amount is:
\[ \text{Total amount} = (x + \text{Overhead}) \times (1 + 0.18) \]
Given that the total amount cannot exceed ₹10,00,000, we can set up the following equation:
\[ (x + \text{Overhead}) \times 1.18 = 10,00,000 \]

Step 2: Apply the formula for overhead and solve for \( x \).
For \( x > ₹5,00,000 \), the overhead is:
\[ \text{Overhead} = 1,00,000 + 0.10(x - 5,00,000) \]
Thus, the total amount becomes:
\[ (x + 1,00,000 + 0.10(x - 5,00,000)) \times 1.18 = 10,00,000 \]
Simplifying:
\[ (x + 1,00,000 + 0.10x - 50,000) \times 1.18 = 10,00,000 \] \[ (1.10x + 50,000) \times 1.18 = 10,00,000 \] \[ 1.298x + 59,000 = 10,00,000 \] \[ 1.298x = 10,00,000 - 59,000 = 9,41,000 \] \[ x = \frac{9,41,000}{1.298} = 7,24,961 \]

Conclusion:
The maximum consulting fee that the employee can charge is ₹7,24,961.