CDS 2026 (I) Elementary Mathematics, question 33

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Q33

A single discount which is equivalent to a series of discounts p%p\%, p2%\frac{p}{2}\%, p4%\frac{p}{4}\% is 31.6%31.6\%. What is the value of pp ?

  1. (a) 24%24\%
  2. (b) 20%20\%Correct answer
  3. (c) 18%18\%
  4. (d) 16%16\%

Solution.

Answer: (b) 20%20\%

  1. The fraction of marked price paid is 1−0.316=0.6841 - 0.316 = 0.684.
  2. Test p=20:(1−0.20)(1−0.10)(1−0.05)=0.8×0.9×0.95=0.684p = 20:(1 - 0.20)(1 - 0.10)(1 - 0.05) = 0.8 \times 0.9 \times 0.95 = 0.684.
  3. This matches exactly.
  4. The paid fraction decreases as p increases across the listed admissible values, so no other listed value works.