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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
