Marks of Arun

Let Arun's marks in Maths be $x$ and in English be $y$ .
$\dfrac{x}{3} = \dfrac{y}{2} + 30\\ 2x - 3y = 180 \longrightarrow \boxed{1}\\ \\ x + y = 240\\ 2x + 2y = 480 \longrightarrow \boxed{2}$
Subtracting $\boxed{1}$ from $\boxed{2}$ , we get:-
$5y = 300\\ y = \color{#69047E}{\boxed{60}}$

nice solution:

Let $x$ be the marks in English. Evidently, marks in mathematics = $240-x$

$\frac{240-x}{3} - \frac{x}{2} = 30$

Multiplying both sides by 6 (LCM of 2 and 3),

$2(240-x) - 3x = 30(6)$

$480 - 2x - 3x = 180$

$5x = 300$

$x = \boxed{60}$

Holla,

let m = mathematics, e = english,

as 1/3 x m = 0.5e + 30,

m /3 = 0.5e + 30

m =1.5e + 90 (1),

m + e = 240 (2), substitute (1) into (2),

1.5e + 90 + e = 240

e = 150 / 2.5 = 60, as english is requested, therefore e = 60,

adios!!!