Daily Math Puzzle: 2026-07-28
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2026-07-28
A cutting-edge AI startup, 'Synapse Solutions', celebrated a phenomenal first year, increasing its revenue by a massive 60% compared to its initial starting point. However, market volatility hit hard in the second year, causing its revenue to plummet by 40% *relative to the first year's peak*. Undeterred, they launched a new product in the third year, which sparked a recovery, boosting revenue by 25% *compared to the second year's reduced level*. What was the overall percentage change in Synapse Solutions' revenue from its initial starting point to the end of the third year?
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Solution
20% increase — Let the initial revenue be R.
At the end of the first year, revenue increased by 60%:
Revenue = R * (1 + 0.60) = 1.6R
At the end of the second year, revenue decreased by 40% relative to the first year's peak:
Revenue = 1.6R * (1 - 0.40) = 1.6R * 0.60 = 0.96R
At the end of the third year, revenue increased by 25% compared to the second year's reduced level:
Revenue = 0.96R * (1 + 0.25) = 0.96R * 1.25 = 1.2R
The overall change from the initial revenue R to the final revenue 1.2R is an increase of 0.2R.
As a percentage, this is (0.2R / R) * 100% = 20% increase.
Common pitfalls include adding/subtracting percentages directly (60 - 40 + 25 = 45%), or applying the final percentage increase to the original base (0.96R + 0.25R = 1.21R, leading to a 21% increase).
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