Total of Arun's marks in Sanskrit and Mathematics together are 80 more than his marks in Science. His average marks in the three subjects are 100. What are his marks in Science?

### Concept & Logic This problem requires forming linear equations based on the textual conditions and substituting one into another. $$ \text{Average} = \frac{\text{Sum of all items}}{\text{Total number of items}} $$ ### Step-by-Step Solution * **Given:** * Let Arun's marks in Sanskrit, Mathematics, and Science be $S$, $M$, and $Sc$ respectively. * Condition 1: $S + M = Sc + 80$ * Condition 2: Average of all three subjects is $100$. * Therefore, $\frac{S + M + Sc}{3} = 100$, which means $S + M + Sc = 300$. * **Calculation:** * We have the sum of all three subjects: $S + M + Sc = 300$. * Substitute the value of $(S + M)$ from Condition 1 into this sum equation. * $(Sc + 80) + Sc = 300$ * Combine like terms: $2Sc + 80 = 300$ * $2Sc = 300 - 80$ * $2Sc = 220$ * $Sc = 110$ ### Exam Strategy & Shortcut Instead of writing out full variables, think in blocks. Let the combined block (Sanskrit + Math) be $X$ and Science be $Y$. You are given $X = Y + 80$ and $X + Y = 300$. Substitute $X$ immediately: $(Y + 80) + Y = 300 \rightarrow 2Y = 220 \rightarrow Y = 110$. This mental grouping saves time writing equations. ### Common Pitfall Choosing "Data inadequate" because there are three variables ($S$, $M$, $Sc$) but seemingly only two equations. The trap is failing to realize that $S$ and $M$ operate as a single combined entity in both given conditions, so their individual values are irrelevant to finding $Sc$. ### Final Answer **Therefore, the correct answer is 110.**