A's marks in Biology are 20 less than 25% of the total marks obtained by him in Biology, Maths and Drawing. If his marks in Drawing be 50, what are his marks in Maths?

### Concept & Logic Translate the word problem into a linear equation with multiple variables. If the number of variables exceeds the number of distinct equations, a unique solution cannot be determined unless further constraints are given. ### Step-by-Step Solution * **Given:** Let A's marks in Biology be $B$, Maths be $M$, and Drawing be $D$. $D = 50$. * **Calculation / Deduction:** * The total marks obtained across all three subjects is $(B + M + 50)$. * The problem states A's marks in Biology ($B$) are 20 less than 25% (or $\frac{1}{4}$) of the total marks. * Set up the equation: $$ B = 0.25(B + M + 50) - 20 $$ * Convert the decimal to a fraction to make it easier to handle: $$ B = \frac{B + M + 50}{4} - 20 $$ * Multiply the entire equation by 4 to eliminate the fraction: $$ 4B = B + M + 50 - 80 $$ * Simplify by grouping variables: $$ 4B - B - M = -30 $$ $$ 3B - M = -30 $$ $$ M = 3B + 30 $$ * We are left with a single linear equation containing two unknown variables ($B$ and $M$). * Because we do not have a second independent equation relating $B$ and $M$, we cannot find a unique numerical value for Maths ($M$). Any value for $B$ will yield a corresponding valid value for $M$. ### Exam Strategy & Shortcut **Variable Counting:** Read the prompt and quickly count unknowns vs equations. You have three subjects (3 unknowns). The prompt gives the value of one subject (1 equation) and a relationship tying the three together (1 equation). You have 2 equations for 3 variables. Mathematically, this guarantees you cannot find a unique solution. You can immediately select "Cannot be determined" without solving the algebra. ### Common Pitfall Students often assume missing information is a typo and try to guess a value for Biology to force an answer, or they misinterpret "total marks" as a standard fixed number (like out of 100 per subject) rather than the sum of obtained marks. Always trust the algebra: if variables remain, the answer is indeterminate. ### Final Answer **Therefore, the correct answer is Cannot be determined.**