The average marks scored by Ravi in English , Science ,Mathematics and History is less than 15 from that scored by him in English , Hsitory , Geography and Mathematics .What is the difference of marks in Science and Geography secured by him ?

Options

A. 40
B. 50
C. 60
D. Date inadequate

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information given.

### Step 1: Define the variables
Let:
- E = Marks in English
- S = Marks in Science
- M = Marks in Mathematics
- H = Marks in History
- G = Marks in Geography

### Step 2: Set up the average equations
According to the problem, the average marks scored by Ravi in English, Science, Mathematics, and History is less than 15 from that scored by him in English, History, Geography, and Mathematics.

1. The average of English, Science, Mathematics, and History:
\[ \text{Average 1} = \frac{E + S + M + H}{4} \]

2. The average of English, History, Geography, and Mathematics:
\[ \text{Average 2} = \frac{E + H + G + M}{4} \]

### Step 3: Set up the inequality
According to the problem, we have:
\[ \frac{E + S + M + H}{4} + 15 = \frac{E + H + G + M}{4} \]

### Step 4: Eliminate the fractions
To eliminate the fractions, multiply the entire equation by 4:
\[ E + S + M + H + 60 = E + H + G + M \]

### Step 5: Simplify the equation
Now, we can simplify the equation by canceling out the common terms (E, H, M) from both sides:
\[ S + 60 = G \]

### Step 6: Rearranging to find the difference
Rearranging the equation gives us:
\[ S - G = -60 \]
This means:
\[ G - S = 60 \]

### Step 7: Conclusion
The difference between the marks in Science and Geography secured by Ravi is:
\[ \text{Difference} = |S - G| = 60 \]

### Final Answer
The difference of marks in Science and Geography secured by Ravi is **60**.

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