Mr. Jones' total annual gross salary, which was ₹ 10 lakhs per year in 2007, was reduced by 10% in 2008. In 2007 his family expenditure for food items was 40% of the total annual gross salary. The prices of average food items increased by 5% between 2007 and 2008. Assuming that the family consumed the same amount of food in 2008, the percentage expenditure on food items, calculated on total annual gross salary in 2008, is

### Concept & Logic This problem is an exercise in tracking **Independent Percentage Changes** on different base values. We need to calculate the new salary and the new food expenditure separately based on their respective changes, and then find the new ratio between them. $$\text{New Percentage} = \left( \frac{\text{New Food Expenditure}}{\text{New Total Salary}} \right) \times 100$$ ### Step-by-step Solution * **Given Information (2007):** * Total Salary in 2007 = ₹ 10,00,000 (10 Lakhs) * Food expenditure in 2007 = $40\%$ of Total Salary * **Calculating 2007 Values:** * Food Expenditure (2007) = $40\%$ of 10,00,000 = $0.4 \times 10,00,000 = ₹ 4,00,000$ * **Calculating 2008 Changes:** * **New Salary (2008):** Salary reduced by $10\%$. $$\text{Salary (2008)} = 10,00,000 \times \left(1 - \frac{10}{100}\right) = 10,00,000 \times 0.9 = ₹ 9,00,000$$ * **New Food Expenditure (2008):** Food prices increased by $5\%$, and consumption is the same, so the total expenditure increases by $5\%$. $$\text{Food Exp (2008)} = 4,00,000 \times \left(1 + \frac{5}{100}\right) = 4,00,000 \times 1.05 = ₹ 4,20,000$$ * **Final Percentage Calculation:** * We need the new food expenditure as a percentage of the new salary. $$\text{Required \%} = \left( \frac{4,20,000}{9,00,000} \right) \times 100$$ $$\text{Required \%} = \left( \frac{42}{90} \right) \times 100$$ $$\text{Required \%} = \left( \frac{7}{15} \right) \times 100$$ $$\text{Required \%} = \frac{700}{15} = 46.66...\%$$ * Rounding to the nearest integer given in the options, we get 47%. ### Exam Strategy & Shortcut **Assume a Base of 100.** The actual value of 10 Lakhs is a distractor and completely unnecessary. Let 2007 Salary = 100 units. 2007 Food = 40 units. 2008 Salary = 100 - 10% = 90 units. 2008 Food = 40 + 5% = 40 + 2 = 42 units. New Percentage = $\frac{42}{90} \times 100 = \frac{420}{9} = 46.66\% \approx 47\%$. This method avoids large numbers and zeros, significantly speeding up calculation. ### Common Pitfall A major time-waster is using the literal "10 Lakhs" figure throughout the calculations. While mathematically correct, it increases the risk of dropping a zero and slows down the process. Whenever asked for a final percentage, relative base values (like 100) are almost always faster and safer. ### Final Answer **Therefore, the correct answer is 47%.**