Question

An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was

Answer 1

Answer:

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Answer 2

Given :

Rate of decline = 10%

Strength of army at last = 729000

To Find : the original strength of the army = ?

Solution :

As we know that

It is lost 10% of its men three times .

So, the number of times = 3

And we will use "Compound interest" method"

$A=P(1-\dfrac{r}{100})^n\\\\729000=P(1-\dfrac{10}{100})^3\\\\729000=P(1-\dfrac{1}{10})^3\\\\729000=P(\dfrac{9}{10})^3\\\\\dfrac{729000\times 1000}{729}=P\\\\10,00,000=P$

Hence, the original strength of army is 10,00,000.