Multiple choice

If p varies directly as q and inversely as square of r, what is the percentage increase in p due to an increase in q by 20% and a decrease in r by 20%?

  1. 87.5%

  2. 85%

  3. 82.5%

  4. 80%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given p = k * q / r^2. If q increases by 20% (q' = 1.2q) and r decreases by 20% (r' = 0.8r), the new p' = k * (1.2q) / (0.8r)^2 = k * 1.2q / 0.64r^2 = (1.2/0.64) * p = 1.875 * p. This represents an 87.5% increase.

AI explanation

By the given conditions of direct and inverse variation, the new value p is proportional to 1.2q divided by the square of 0.8r. Calculating the denominator gives 0.64, so the new multiplier is 1.2 / 0.64, which is 1.875. This represents an 87.5% increase in p.

Keep practicing — related questions