An army lost 10% of its men in war. Then 10% of the remaining men died due to disease, and then 10% of the rest were declared disabled. After these three successive reductions, the army was left with 7,29,000 active men. What was the original strength of the army?

Introduction / Context:This problem tests successive percentage reduction. When percentages are applied one after another, you multiply the remaining fractions, not subtract the percentages directly from the original. Here, three separate 10% reductions happen sequentially.

Given Data / Assumptions:

• First reduction: 10% lost in war (remaining 90%).
• Second reduction: 10% of remaining died (remaining 90% of the remainder).
• Third reduction: 10% of the rest disabled (remaining 90% again).
• Final active men = 729,000.

Concept / Approach:Each 10% reduction means multiply by 0.9. After three steps, final = original * 0.9 * 0.9 * 0.9 = original * 0.9^3. Solve original = final / 0.9^3.

Step-by-Step Solution:

Verification / Alternative check:If original is 1,000,000: after first 10% loss remaining 900,000; after next 10% remaining 810,000; after next 10% remaining 729,000, matching the final count.

Why Other Options Are Wrong:

Common Pitfalls:Subtracting 30% from the original directly (incorrect), or applying 10% each time to the original rather than to the remaining strength.

Final Answer:1,000,000