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A number is first decreased by 20% and then increased by 15%. The number so obtained is 64 less than the original number. The original number is :

  • A.850
  • B.750
  • C.700
  • D.800

Answer: D

The original number is 800.

Decreasing by 20% and then increasing by 15% multiplies the number by \(0.8 \times 1.15 = 0.92\). The result is 8% less than the original, and that 8% equals 64:

\[ 0.08N = 64 \Rightarrow N = 800 \]

Check: 800 falls to 640, then rises to 736, which is 64 less than 800. 850, 750 and 700 give differences of 68, 60 and 56.

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