When 5 percent of maize is lost in grinding, a country must import 20 million bags to meet its needs, but when only 2 percent is lost in grinding, it needs to import only 15 million bags; find the total quantity of maize, in million bags, that actually grows in the country.

Introduction / Context:
This problem combines percentage loss with supply and import data, which is common in arithmetic reasoning and data interpretation questions. The key idea is that the country has a fixed internal production of maize, a certain percentage of which is lost during grinding. The remaining portion plus imports must meet the same total demand in both scenarios. By setting up equations for the two different loss percentages, we can solve for the original quantity of maize produced in the country.

Given Data / Assumptions:
- Let the total maize produced in the country be Q million bags.
- In the first situation, 5 percent is lost in grinding, so 95 percent of Q is usable.
- Under 5 percent loss, the country needs to import 20 million bags to meet total demand.
- In the second situation, only 2 percent is lost, so 98 percent of Q is usable.
- Under 2 percent loss, the country imports only 15 million bags.
- The total maize demand is assumed constant in both cases.

Concept / Approach:
The demand for maize can be expressed in two ways: as domestic usable production plus imports in each scenario. Because total demand does not change, these two expressions must be equal. This leads to a linear equation in Q. The core concept is balancing supply with losses and extra imports. Express percentages as decimals to make the algebra straightforward, and then solve for Q. Finally, convert the fraction to a mixed number or decimal that matches one of the options.

Step-by-Step Solution:
Step 1: Under 5 percent loss, usable domestic production is 95 percent of Q, which is 0.95 * Q. Step 2: With 5 percent loss, the country imports 20 million bags, so total demand D can be written as D = 0.95 * Q + 20. Step 3: Under 2 percent loss, usable domestic production is 98 percent of Q, which is 0.98 * Q. Step 4: With 2 percent loss, the country imports 15 million bags, so the same demand D can be written as D = 0.98 * Q + 15. Step 5: Since total demand is unchanged, set the two expressions equal: 0.95 * Q + 20 = 0.98 * Q + 15. Step 6: Rearrange the equation: 20 - 15 = 0.98 * Q - 0.95 * Q, which simplifies to 5 = 0.03 * Q. Step 7: Solve for Q by dividing both sides by 0.03 to get Q = 5 / 0.03 = 500 / 3. Step 8: Convert 500 / 3 to a mixed number: 500 / 3 = 166 2/3. Thus the country produces 166 2/3 million bags of maize.

Verification / Alternative check:
Check the first scenario: With Q = 166 2/3, 5 percent loss equals (5 / 100) * 166 2/3, and 95 percent usable is (95 / 100) * 166 2/3 = (19 / 20) * (500 / 3) = 475 / 3. Adding imports of 20 gives total demand D = 475 / 3 + 20 = 475 / 3 + 60 / 3 = 535 / 3. Check the second scenario: 2 percent loss leaves 98 percent usable, which is (98 / 100) * 166 2/3 = (49 / 50) * (500 / 3) = 490 / 3. Adding imports of 15 gives D = 490 / 3 + 15 = 490 / 3 + 45 / 3 = 535 / 3. Both cases yield the same demand, confirming that the computed Q is correct.

Why Other Options Are Wrong:
Option 188 million: Substituting 188 into the equations will not make the total demand equal in both loss scenarios.
Option 192 3/4 million: This value does not satisfy the balance equation and leads to different demands under 5 percent and 2 percent loss.
Option None of these: Since we have found a value, 166 2/3 million, that exactly fits the condition, this option is incorrect.
Option 200 million: This round figure may look attractive but does not satisfy the equality of total demand in both scenarios.

Common Pitfalls:
Learners may confuse percentage loss with percentage of maize remaining, or mistakenly write 5 percent remaining instead of 95 percent. Another frequent error is to treat the imports as part of the loss instead of additional supply. Some also forget that the demand is constant and fail to equate the two demand expressions. Careful interpretation of the words and methodical algebra prevent these mistakes.

Final Answer:
The quantity of maize that grows in the country is 166 2/3 million bags.