Question

The ratio of marks obtained by x and y is 3:2. if x gets 30 marks more than y, find their individual marks.

Answer 1

$\text{ratio of marks obtained by x and y} = 3 : 2 \\ \implies \frac{x}{y} = \frac{3}{2} \\ \implies 2x = 3y \\ \implies x = \frac{3y}{2} ....1 \\ \\ \text{x gets 30 marks more than y} \\ \implies x-30 = y ~ .....2 \\ \\ \text{putting value of x from equation 1 in 2}\\ \implies \frac{3y}{2} - 30 = y \\ \implies \frac{3y - 60}{2} = y \\ \implies 3y - 60 = 2y\\ \implies y = 60 \\ \text{Therefore} ~ x = 60+30 = 90 (\text{from equation 1})\\ \text{So, x got 90 marks and y got 60 marks.} \:$