1. 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.
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By: anil on 05 May 2019 01.21 am
Let the original strength = $$100x$$ Men remaining after war = $$100x - frac{10}{100} imes 100x = 90x$$ Men remaining after diseases = $$90x - frac{10}{100} imes 90x$$ = $$90x - 9x = 81x$$ Men remaining excluding the disabled = $$81x - frac{10}{100} imes 81x$$ = $$81x - 8.1x = 72.9x$$ Acc to ques, => $$72.9x = 729000$$ => $$x = frac{729000}{72.9} = 10000$$ $$ herefore$$ Original strength of men = $$100 imes 10,000 = 1,000,000$$
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