Question

The HCF and LCM of two numbers x and y is 6 and 210 respectively. If x + y = 72, which of the following relation is correct?

(a) \(\frac 1x +\frac 1y=\frac{3}{35}\)

(b) \(\frac 1x +\frac 1y=\frac{2}{35}\)

(c) \(\frac 1x +\frac 1y=\frac{35}{2}\)

(d) not sufficient

Answer 1

Correct option : (b) \(\frac 1x +\frac 1y=\frac{2}{35}\)

\(x + y = 72\)  ......(1)

= Product of numbers = HCF \(\times\) LCM

\(\Rightarrow\) \(xy =6 \times 210 =1260\)    ........(2)

Divide equation (1) by (2), we get

\(\frac{x+y}{xy} =\frac{72}{1260}\)

\(\Rightarrow \frac{1}{x} + \frac{1}{y} =\frac{2}{35}\).