Question

A number is given three successive discounts of 20%, 25% and 20%; Three successive increases of 20%, 25% and 20% are made to the resulting number, resulting in a number that differs from the original by 408 units. Calculate the original number.

Answer 1

3000

Explanation:

The multiplier associated with each percentage change (p) is (1 +p). We can use this fact to relate the original number to the modified number.

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discounted number

Let x represent the original number. Then the discounted number is ...

x(1 -20%)(1 -25%)(1 -20%) = x(0.8)(0.75)(0.8) = 0.48x

increased number

After those discounts, the increased number is ...

(0.48x)(1 +20%)(1 +25%)(1 +20%) = (0.48x)(1.2)(1.25)(1.2) = 0.864x

difference

The difference from the original is ...

x - 0.864x = 408

0.136x = 408 . . . . simplify

x = 3000 . . . . . . . divide by the coefficient of x

The original number was 3000.