Question 51

If x% of y is 1% of z, y% of z is 1% of x and z% of x is 1% of y, then the value of xy + yz + zx is

Solution

x% of y is 1% of z

$$\frac{x}{100} * y = \frac{1}{100} * z$$

xy = z ....... (1)

y% of z is 1% of x

$$\frac{y}{100} * z = \frac{1}{100} * x$$

yz = x ....... (2)

z% of x is 1% of y

$$\frac{z}{100} * x = \frac{1}{100} * y$$

zx = y ....... (3)

Now,

xy + yz + zx = z + x + y

Put value of z from equation (1) in equaiton (2):

y * xy = x

$$y^2 = 1$$

y = 1 Similarly,

x = z = 1

Hence, x + y + z = 1 + 1 + 1 = 3

Share on Whatsapp Share on Whatsapp