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One more quest from %

by engg.manik » Mon Sep 28, 2009 4:09 am
q---> a company sells z numbers of products, price of each product is y. In order to have revenue unchange by what percentage should the sales increase if the price falls down by 20%.

Can someone explain how to hit these kind of questions.
Thanks in advance.
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by mp2437 » Mon Sep 28, 2009 6:09 am
See example you posted earlier. In general,

R = z*y, where R is revenue. If you want to have the same R, and you decrease one variable, the other must increase to compensate. Therefore:

R = z * y
R = z * (1 + x) * y (1 - .2), where x is the percentage increase that is necessary to compensate.

It is always better to use numbers for examples like these, so lets use 100, and z = 25, y = 4.

Since y is going down by 20%, its new price is 4*(1-.2) = 3.20. Now you know that R = 100 (since it is unchanged), and a new price of 3.20, so you could find z by:

R = z_new * y_new --> z_new = R / y_new = 100 / 3.20 = 31.25.

so z goes from 25 to 31.25. The percent increase is equal to (31.25 - 25)/25 = 25%.
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