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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The marginal revenue of a firm is MR = 100 − 4x, where x is the number of units sold, and total revenue is zero when no units are sold. The firm's marginal cost is MC = 40 + 2x. Using integration, the additional profit gained by increasing output from 0 up to the output where MR = MC is:

Setting marginal revenue equal to marginal cost gives an output of 10 units. Integrating the difference, 60 minus 6x, from 0 to 10 gives 600 minus 300, so the additional profit is ₹300.

  1. A₹200
  2. B₹300Correct
  3. C₹400
  4. D₹500

Explanation

MR = MC gives 100 − 4x = 40 + 2x, so x = 10. Added profit = ∫ from 0 to 10 of (MR − MC) dx = ∫(60 − 6x) dx = [60x − 3x²] = 600 − 300 = 300. Check: the integrand falls linearly from 60 to 0, so the area is a triangle: ½ × 10 × 60 = 300. Option ₹400 would wrongly use only 60x − 2x² ignoring the correct coefficient.

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