Question 8

The HCF and LCM of two numbers x and y are respectively 6 and 210.
If x + y = 72, then $$\frac{1}{x}+\frac{1}{y}$$ is equal to.

Solution

The HCF and LCM of two numbers x and y are respectively 6 and 210.

$$x\times y=HCF\times LCM$$

$$xy=1260$$

$$x=\dfrac{1260}{y}$$

It is given that $$x+y=72$$

$$y+\dfrac{1260}{y}=72$$

$$y^2-72y+1260=0$$

$$y^2-42y-30y+1260=0$$

Thus, y = 42 or 30. Then, x = 30 or 42.

$$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{42}+\dfrac{1}{30}=\dfrac{7+5}{210}=\dfrac{2}{35}$$

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