Mathematics 2015 JAMB Past Questions - Question 40: If x varies directly as the square of P and inversely as Q and x=25 when P=4 and Q=2 ,Find x when P=6 and Q=3

Correct Answer

D

Explanation

x=kp2/Q ,25=k(4)2/2k=25/8 ,x=25p2/8Qx=25*62/8*3x=75/2=37.5To solve this problem, we can use the formula for direct and inverse variation, which is \(x = k \frac{P^2}{Q}\), where k is the constant of variation.First, we can find the value of k using the initial values given:\(25 = k \frac{4^2}{2}\)\(25 = k \frac{16}{2}\)\(25 = 8k\)\(k = \frac{25}{8}\)Now that we have the value of k, we can use it to find x when P=6 and Q=3:\(x = \frac{25}{8} \frac{6^2}{3}\)\(x = \frac{25}{8} \frac{36}{3}\)\(x = \frac{25}{8} \times 12\)\(x = 25 \times 3\)\(x = 75\)So, when P=6 and Q=3, x equals 75.