Ram got twice as many marks in English as in Science. His total marks in English, Science and Maths are 180. If the ratio of his marks in English and Maths is `2 : 3`, what is his marks in Science ?

Options

A. 30
B. 60
C. 72
D. 90

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Define Variables
Let the marks in Science be represented as \( S \). According to the problem, Ram got twice as many marks in English as in Science. Therefore, we can express the marks in English as:
\[ E = 2S \]

### Step 2: Establish the Ratio of English to Maths
We are given that the ratio of marks in English to Maths is \( 2:3 \). Let the marks in Maths be represented as \( M \). From the ratio, we can express Maths in terms of English:
\[ \frac{E}{M} = \frac{2}{3} \]
This implies:
\[ M = \frac{3}{2}E \]

### Step 3: Substitute the Value of E
Now, substitute the value of \( E \) (which is \( 2S \)) into the equation for \( M \):
\[ M = \frac{3}{2}(2S) = 3S \]

### Step 4: Write the Total Marks Equation
According to the problem, the total marks in English, Science, and Maths is 180. Therefore, we can write:
\[ E + S + M = 180 \]
Substituting the expressions for \( E \) and \( M \):
\[ 2S + S + 3S = 180 \]

### Step 5: Combine Like Terms
Combine the terms on the left side:
\[ 6S = 180 \]

### Step 6: Solve for S
Now, divide both sides by 6 to find \( S \):
\[ S = \frac{180}{6} = 30 \]

### Conclusion
Thus, the marks in Science are:
\[ \boxed{30} \]

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