The marks obtained by Suresh in English, mathematics and science are in the ratio (1/2) : (1/3) : (3/5). If his total score is 860, his marks in English are

The marks obtained by Suresh in English, mathematics and science are in the ratio (1/2) : (1/3) : (3/5). If his total score is 860, his marks in English are
1). 160
2). 300
3). 228
4). 312

Let the marks in English, Mathematics, and Science be $\frac{1}{2}x$, $\frac{1}{3}x$, and $\frac{3}{5}x$ respectively.
Given:
$\frac{1}{2}x + \frac{1}{3}x + \frac{3}{5}x = 860$
Find the LCM of $2, 3, 5$:
LCM$(2, 3, 5) = 30$
Multiply throughout by $30$ to eliminate fractions:
$ \left( \frac{30}{2}x \right) + \left( \frac{30}{3}x \right) + \left( \frac{30}{5} \times 3x \right) = 860 \times 30$
$ 15x + 10x + 18x = 860 \times 30$
$ 43x = 25800$
Solve for $x$:
$x = \frac{25800}{43} = 600$
Marks in English:
$\frac{1}{2} \times 600 = 300$

Final Answer: **$300$** 

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