The respective ratio between the monthly salaries of Rene and Som is 5 : 3. Out of her monthly salary Rene gives 1/6th as rent, 1/5th to her mother, 30% as her education loan and keeps 25% aside for miscellaneous expenditure. Remaining ₹ 5000 she keeps as savings. What is Som's monthly salary?

### Concept & Logic To find the total salary from scattered fractional and percentage expenses, first unify all expenses into a single format (either all fractions or all percentages), sum them up, and subtract from the whole to find the fractional representation of the remaining savings. ### Step-by-Step Solution 1. Let Rene's salary be $5x$ and Som's salary be $3x$. 2. Calculate total expenses of Rene as fractions of her salary: - Rent = $\frac{1}{6}$ - Mother = $\frac{1}{5}$ - Education Loan = $30\% = \frac{30}{100} = \frac{3}{10}$ - Misc = $25\% = \frac{25}{100} = \frac{1}{4}$ 3. Total expenses fraction = $\frac{1}{6} + \frac{1}{5} + \frac{3}{10} + \frac{1}{4}$. - Find the LCM of denominators (6, 5, 10, 4) which is 60. - Total expenses = $\frac{10}{60} + \frac{12}{60} + \frac{18}{60} + \frac{15}{60} = \frac{55}{60} = \frac{11}{12}$. 4. Find the remaining savings fraction: - Savings fraction = $1 - \text{Total Expenses} = 1 - \frac{11}{12} = \frac{1}{12}$. 5. We are given that Rene's savings amount to ₹ 5000: - $\frac{1}{12} \times (\text{Rene's Salary}) = 5000$ - Rene's Salary ($5x$) = $5000 \times 12 = 60000$. 6. Now, solve for $x$ and find Som's salary: - $5x = 60000 \implies x = 12000$. - Som's salary = $3x = 3 \times 12000 = 36000$. ### Exam Strategy & Shortcut Convert everything to percentages for mental math if you are comfortable: $\frac{1}{6} \approx 16.66\%$, $\frac{1}{5} = 20\%$. Total expenses = $16.66\% + 20\% + 30\% + 25\% = 91.66\%$. Savings = $100\% - 91.66\% = 8.33\% = \frac{1}{12}$. If $\frac{1}{12}$ is 5k, Total is 60k. 5 parts = 60k, 1 part = 12k. Som's 3 parts = 36k. ### Common Pitfall A common error is confusing successive percentages with additive percentages. The problem says "out of her monthly salary" for each item, which means they are all calculated on the base total salary, not on the "remaining" balance after each expense. ### Final Answer Therefore, the correct answer is **₹36000**.