Question

Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?

Answer 1

The product decreases 2022.

Explanation:

(x + 1)(y - 1) = xy + 2020

xy - x + y - 1 = xy + 2020

-x + y = 2021

(x - 1)(y + 1) = xy + x - y - 1

+ 2021 = -x + y

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(x - 1)(y + 1) + 2021 = xy - 1

(x - 1)(y + 1) = xy - 2022

The product decreases 2022.