When a block of iron floats in mercury at $\;0^{0}C\;$ , a fraction $\;K_{1}\;$ of its volume is submerged. While at the temperature $\;60^{0}C\;$ , a fraction $\;K_{2}\;$ is seen submerged . If the coefficient of volume expansion of iron is $\;r_{Fe}\;$ and that of mercury is $\;r_{Hg}\;$ , then the ratio $\;\large\frac{K_{1}}{K_{2}}\;$ can be expanded as

Question

$(a)\;\large\frac{1+60 r_{Fe}}{1+60 r_{Hg}}\qquad(b)\;\large\frac{1-60 r_{Fe}}{1+60 r_{Hg}}\qquad(c)\;\large\frac{1+60 r_{Fe}}{1-60 r_{Hg}}\qquad(d)\;\large\frac{1+60 r_{Hg}}{1+60 r_{Fe}}$