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GATE 2025 EC GA Q.10: solution and answer

GATE 2025 · ECGA Q.10 · 2 marks · MCQ

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 Rs. 5,00,000. For higher fees, the overhead is Rs. 1,00,000 plus 10% of the amount by which the fee exceeds Rs. 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 Rs. 10,00,000, what is the maximum consulting fee that the employee can charge?

  1. (A)

    Rs. 7,01,438

  2. (B)

    Rs. 7,24,961

  3. (C)

    Rs. 7,51,232

  4. (D)

    Rs. 7,75,784

See the question in the paper
GATE 2025 EC GA question 10Tap to open full size

Answer and solution

ANSWER

The maximum consulting fee is Rs. 7,24,961, option (B).

Official answer: BSource: Official answer key, GATE 2025 EC (IIT Roorkee)

  1. Decide which slab applies. If the fee , the overhead is , so the client pays . That is well under the Rs. limit, so the maximum fee must be above Rs. .

  2. Overhead in the upper slab (the fixed part plus 10% of the excess): .

  3. Fee plus overhead: .

  4. GST of 18% multiplies this pre-tax amount by , so the client pays , and this must satisfy .

  5. Remove the tax first: .

  6. Solve for the fee: .

  7. Check with : overhead , pre-tax total , and . Of the options, (A) is affordable but is not the maximum, while (C) and (D) take the bill past Rs. (Rs. and Rs. ). So the maximum fee is Rs. , option (B).

KEY IDEA

First work out which slab applies. Even at the top of the first slab (fee Rs. 5,00,000) the client pays only Rs. 7,08,000, so the fee must be in the upper slab. There the overhead is 0.1F + 50,000, so the client pays 1.18(1.1F + 50,000). Set that equal to Rs. 10,00,000 and work backwards: take out the 18% GST first, then the overhead.

WATCH OUT FOR

One mistake is to charge the 10% on the whole fee instead of only on the part above Rs. 5,00,000, which gives an overhead of 1,00,000 + 0.1F. Another is to use the 20% slab rate for the whole fee. A third is to take 18% off the Rs. 10,00,000 (multiplying by 0.82) instead of dividing by 1.18. Each of these moves the answer away from (B) and can land near one of the other options.

From the GATE 2025 EC paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

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