x varies directly as y and x varies indiretly as the square of z.
Posted on 17-02-2023
Ques - x varies directly as y and x varies indiretly as the square of z. When y = 75 and x = 6, then z = 5. Find the value of x when y = 24 and z = 4.
(a) 1
(b) 2
(c) 3
(d) 4
Solution -
x varies directly as y = x ∝ y
x varies indiretly as the square of z = x ∝ 1/z2
So,
x ∝ y/z²
Remove the sign of proportional and and a constent k.
Therefore,
x =ky/z² ___________ (1)
Now,
Put the value of x, y, z in eq. 1.
6 = k(75)/(5)²
6 = k(75)/(25)
6 = 3k
k = 2
Again,
Put the value of k = 2, y = 24 and z = 4 in eq. 1.
x =ky/z²
x = 2(24)/(4)²
x = 48/16
x = 3
Hence,
The correct answer is option (c) 3.
Thank You