Answer:
Option (E)
Step-by-step explanation:
[tex]\frac{a}{b}=\frac{c}{d}=k[/tex]
[tex]\frac{a}{b}=k[/tex]
[tex]b=\frac{a}{k}[/tex] ------(1)
[tex]\frac{c}{d}=k[/tex]
[tex]d=\frac{c}{k}[/tex] -------(2)
Since, [tex]\frac{6a+24}{md+6b}=k[/tex]
By substituting the values of b and d from equation (1) and (2),
[tex]\frac{6a+24}{\frac{mc}{k}+\frac{6a}{k}}=k[/tex]
[tex]\frac{k(6a+24)}{6a+mc}=k[/tex]
[tex]\frac{6a+24}{6a+mc}=1[/tex]
6a + 24 = 6a + mc
mc = 24
m = [tex]\frac{24}{c}[/tex]
Therefore, Option (E) will be the correct option.
