Question 50

An army lost 10% its men in war, 10% of the remaining due to diseases and 10% of the rest were disabled. Thus, the strength was reduced to 729000 active men. Find the original strength.

Solution

Let the original strength = $$100x$$

Men remaining after war = $$100x - \frac{10}{100} \times 100x = 90x$$

Men remaining after diseases = $$90x - \frac{10}{100} \times 90x$$

= $$90x - 9x = 81x$$

Men remaining excluding the disabled = $$81x - \frac{10}{100} \times 81x$$

= $$81x - 8.1x = 72.9x$$

Acc to ques,

=> $$72.9x = 729000$$

=> $$x = \frac{729000}{72.9} = 10000$$

$$\therefore$$ Original strength of men = $$100 \times 10,000 = 1,000,000$$

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