The total monthly salary of 4 men and 2 women is ₹ 46,000. If a woman earns ₹ 500 more than a man, what is the monthly salary of a woman?

### Concept & Logic Translate the textual relationships into a system of linear equations. Use the substitution method to replace one variable and solve entirely for the target variable. ### Step-by-Step Solution * **Given:** * Let a man's salary be $M$ and a woman's salary be $W$. * $4M + 2W = 46000$ * $W = M + 500 \Rightarrow M = W - 500$ * **Calculation:** 1. Substitute the expression for $M$ into the total salary equation. We substitute for $M$ because we want to solve directly for $W$: $4(W - 500) + 2W = 46000$ 2. Expand the equation: $4W - 2000 + 2W = 46000$ 3. Combine like terms: $6W = 48000$ 4. Solve for $W$: $W = 48000 / 6 = 8000$ ### Exam Strategy & Shortcut Use the options to back-solve, keeping the equations mental. Assume a woman earns ₹ 8000 (Option c). Then a man earns $8000 - 500 = 7500$. Check the total: $4(7500) + 2(8000) = 30000 + 16000 = 46000$. This matches the condition perfectly, confirming ₹ 8000 is the correct answer without rigorous algebra. ### Common Pitfall A frequent trap is substituting $W$ with $(M + 500)$, solving for $M$, finding $M = 7500$, and mistakenly selecting option (b) if in a rush. Always ensure you are solving for the specific variable requested in the final question. ### Final Answer **Therefore, the correct answer is ₹ 8000.**