Question : Rohan scored twice as many marks in English as he did in Science. His total marks in English, Science, and Mathematics are 126. If the ratio of his marks in English and Mathematics is 2 : 3, his marks in English are:
Option 1: 63
Option 2: 20
Option 3: 21
Option 4: 42
Correct Answer: 42
Solution :
Let us denote marks of Rohan in English, Science, and Mathematics be E, S, and M, respectively.
Given, $\text{E=2S}$
And, $\text{E + S + M} = 126$
The ratio of his marks in English and Mathematics is 2 : 3.
From $\text{E + S + M} = 126$, we can get $\text{2S + S + M} = 126$ [Using $\text{E = 2S}$]
⇒ $3\text{S} + \text{M} = 126$----------(1)
Now, $\frac{\text{E}}{\text{M}} = \frac{2}{3}$
$\frac{\text{2S}}{\text{M}}=\frac{2}{3}$
⇒ $\text{M} = \text{3S}$
Putting this value in (1), we get,
$\text{3S + 3S}=126$
⇒ $\text{6S}=126$
⇒ $\text{S}= 21$
$\therefore\text{E}=\text{2S}=2\times21 = 42$
Hence, the correct answer is 42.
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