Question
An army lost 20% its men in war, 20% of the remaining
due to diseases and 20% of the rest were disabled. Thus, the strength was reduced to 64,000 active men. Find the original strength.Solution
Let the original strength of men in army = x Then, lost in war Rest men = x - (20 × x)/100 = 4x/5 Now, loss of men due to disease, rest men = 4x/5 - 4x/5 × 20/100 = (16 x)/25 Now, after disabled, rest men = (16 x)/25 - (16 x)/25 × 20/100 = (64 x)/125 Now, according to the question, (64 x)/125 = 64,000 x = 1,25,000
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