**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/z^{2}

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