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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The demand function is p = 20 − x and the supply function is p = 4 + x, with p in ₹ and x in units. The consumer's surplus at the equilibrium price is:

Equilibrium occurs at x = 8 and price ₹12. Consumer's surplus is the integral of demand from 0 to 8, which is 128, minus total payment 8 × 12 = 96. The consumer's surplus therefore equals ₹32.

  1. A₹32Correct
  2. B₹64
  3. C₹16
  4. D₹48

Explanation

Equilibrium: 20 − x = 4 + x gives x = 8, p = 12. Consumer's surplus = ∫ from 0 to 8 of (20 − x) dx − 8×12 = [20x − x²/2] = 160 − 32 = 128, minus 96 = 32. The figure 64 arises from forgetting the 1/2 in x²/2 term handling (using the area as rectangle-triangle error).

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