Given that y is directly proportional to x.
[tex] \sf y \propto x[/tex]
[tex]\longrightarrow \sf y = k \times x[/tex]
[tex]\\[/tex]
At first, we must find the value of k.
We have a relation given between 'x' and 'y' (that is, when 'x' is 75, 'y' is 60). We can call that Case - 1.
[tex]\sf 60 = k \times 75[/tex]
[tex]\longrightarrow \sf k = \dfrac{60}{75}[/tex]
[tex]\longrightarrow \sf k = \dfrac{4}{5}[/tex]
[tex]\\[/tex]
Now, we have to find 'x' when 'y' is 480. We can call that Case - 2.
[tex]\sf y = k \times x [/tex]
We are having the value of 'y' and 'k'.
[tex]\longrightarrow \sf 480 = \dfrac{4}{5} \times x[/tex]
[tex]\longrightarrow \sf x = 480 \times \dfrac{5}{4}[/tex]
[tex]\longrightarrow \sf x = 120 \times 5[/tex]
[tex]\leadsto \underline{\boxed{\sf {\pink{x = 600}}}}[/tex]
