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Gains and losses that pair off

Mental mathHard

A book of $800$ gains $25%$ , then loses $20%$ , then gains $25%$ , and so on, alternating for $6$ periods in total. Each move applies to the latest value. What is the final value?

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Hint

Look at what one gain and one loss do together.

Solution

One gain and one loss multiply by $1.25 \times 0.8$ .
$1.25 \times 0.8 = 1$ , so each pair returns the book to its starting value.
$6$ periods form $3$ such pairs.
So the final value is $800$ .

Answer: $800$

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