Prices of foodgrains have risen by 10% and of other items of consumption by 15%. If the ratio of an employee's expenditure on foodgrains and other items is 2 : 5, by how much should his salary be increased so that he may maintain the same level of consumption as before, assuming that his present salary is ₹ 3500?

### Concept & Proportional Distribution When an overall total is divided in a given ratio, you can find the absolute value of each part. The net increase required is the sum of the absolute increases of each individual component. $$\text{Net Increase} = \text{Increase in Part 1} + \text{Increase in Part 2}$$ ### Step-by-Step Solution 1. **Given:** Total salary = ₹ 3500. Expenditure ratio (Foodgrains : Other items) = $2 : 5$. 2. **Calculate Absolute Expenditures:** Total ratio parts = $2 + 5 = 7$ parts. Value of 1 part = $\frac{3500}{7} = 500$. Expenditure on foodgrains = $2 \text{ parts} \times 500 = 1000$. Expenditure on other items = $5 \text{ parts} \times 500 = 2500$. 3. **Calculate the Increase for Each Category:** Price of foodgrains rises by $10\%$. Increase = $10\%$ of $1000 = \frac{10}{100} \times 1000 = 100$. Price of other items rises by $15\%$. Increase = $15\%$ of $2500 = \frac{15}{100} \times 2500 = 375$. 4. **Calculate Total Required Salary Increase:** Total increase needed = $100 + 375 = 475$. ### Exam Strategy & Shortcut Calculate the net percentage increase directly using the weighted average of the percentages based on the ratio parts: Net % increase = $\frac{(2 \times 10) + (5 \times 15)}{2 + 5} = \frac{20 + 75}{7} = \frac{95}{7}\%$. Required increase amount = $\frac{95}{700} \times 3500 = 95 \times 5 = 475$. ### Common Pitfall A common mistake is averaging the two percentages directly (getting $12.5\%$) and applying it to the total salary, completely ignoring the $2:5$ weighting ratio. ### Final Answer Therefore, the correct answer is **₹ 475**.