GATE ECE 2025 | GA | Question: 10

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 of $18 \%$ on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., 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. ₹$7,01,438$
• B. ₹$7,24,961$
• C. ₹$7,51,232$
• D. ₹$7,75,784$

Answer 1

Since 10L is total amount it includes overhead consulting fees & 18% gst taking consulting + overhead as X then 18% gst on it becomes 1.18 of x

1.18 x = 10L

finding x willl give 847457.7

now its given that 1L is overhead subtracting that we get 747457.7  .

Question says 10% overhead on amount more than 5L so here if you take it 7L then 10% overhead on 7l - 5L i.e on 2L

keeping this in mind we can now do option elimination

 

10% of 7,01,438-5L + 7,01,438 is still less than our 747457.7  so Option A is not our answer

10% OF 7,51,232 + 7,51,232 is much more than what we got 747457.7   so Option C & D are not are answers

 

this leaves B and that is our answer.

 

Answer 2

Solve in reverse,

$x + 0.18 \leq 10^6$

$x \leq \frac{10^8}{118}$ , the maximum ammount employee can have after paying $18\%$ GST

By the options given, charged fee is definitely greater then $5,00, 000$ that means the overhead is $10^5 + 10\%$ of exceeded ammount.

 

Assume $y$ is the ammount that employee charged so overhead = $10^5 + (y - 5*10^5)\frac{10}{100}$

$y + 10^5  + (y - 5*10^5)\frac{10}{100} \leq \frac{10^8}{118} $

$y \leq 7,24,961.48$