[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{Total Number of fish } [/tex][tex]\sf = 30 [/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{ Number of carp fish } [/tex][tex]\sf = 9 [/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ Ratio of carp to sticklebacks to tench } [/tex][tex]\sf in \:the \:pond[/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\longrightarrow[/tex]Number of fish that are not carp = Total fish - number of carp fish
[tex]\begin{gathered}\implies\quad \sf 30-9 \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 21 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Since 1/3 of remaining fish which are not carp are sticklebacks , Number of sticklebacks =
[tex]\begin{gathered}\implies\quad \sf \frac{1}{3} \times number \:of \:remaining \: fish\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf \frac{1}{3}\times 21 \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 7 \\\end{gathered} [/tex]
Now ,
[tex]\longrightarrow[/tex]Number of tench = Total number of fish - (Number of carp + Number of sticklebacks)
[tex]\begin{gathered}\implies\quad \sf 30-(9+7) \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 30-16\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 14\\\end{gathered} [/tex]
[tex]\therefore[/tex]Ratio of carp to sticklebacks to tench in the pond =
[tex]\begin{gathered}\quad\quad \boxed{\sf {9: 7:14}} \\\end{gathered} [/tex]
