When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is:

### Concept & Logic This problem utilizes the concept of constant totals and absolute differences. The total production of wheat remains constant. The difference in the amount available for export is directly and solely caused by the difference in the grinding loss percentages. $$ \text{Difference in Export} = \text{Difference in Loss \%} \times \text{Total Production} $$ ### Step-by-step Solution **Given:** Scenario 1: 15% loss results in 30 lakh tons export. Scenario 2: 10% loss results in 40 lakh tons export. Let the total production of wheat be $x$ lakh tons. Determine the difference in the loss percentages: $$ 15\% - 10\% = 5\% $$ This 5% difference in loss directly accounts for the difference in the export volumes. Determine the difference in export volumes: $$ 40 \text{ lakh tons} - 30 \text{ lakh tons} = 10 \text{ lakh tons} $$ Set up the relationship: $$ 5\% \text{ of Total Production} = \text{Difference in Exports} $$ $$ 5\% \text{ of } x = 10 $$ Solve for $x$: $$ \frac{5}{100} \times x = 10 $$ $$ \frac{1}{20} \times x = 10 $$ $$ x = 10 \times 20 = 200 $$ ### Exam Strategy & Shortcut Use the **Percentage Gap Strategy**. The gap in percentages is 5% (15% vs 10%). The gap in real values is 10 lakh tons (40 vs 30). Therefore, 5% of the total = 10. To find 100% (the total production), simply multiply both sides by 20. $ 5\% \times 20 = 100\% $. $ 10 \times 20 = 200 $. The total production is 200 lakh tons. You can solve this entirely in your head in 5 seconds. ### Common Pitfall A tedious misstep is trying to set up individual complex equations for each scenario like $ x - 0.15x = 30 + \text{domestic consumption} $. The problem doesn't mention domestic consumption, but the difference between production and export implies it exists. Focus strictly on the *change* between scenarios to bypass unknown variables. ### Final Answer **Therefore, the correct answer is 200 lakh tons.**