The value of an item depreciates $x\%$ per year. The present value of the item is $₹ 109350$. Its value after 3 years will be $₹ 79716.15$. Two years ago from now, its value, in rupees, was

The value of an item depreciates $x\%$ per year. The present value is $₹ 109350$, and after 3 years it will be $₹ 79716.15$.

Using the depreciation formula:

$A = P\left(1 - \frac{x}{100}\right)^n$

where $A$ is the final value, $P$ is the initial value, $x$ is the rate of depreciation, and $n$ is the time in years.

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$79716.15 = 109350 \left(1 - \frac{x}{100}\right)^3$

$\left(1 - \frac{x}{100}\right)^3 = \frac{79716.15}{109350}$

$\left(1 - \frac{x}{100}\right)^3 = \frac{7971615}{10935000}$

$\left(1 - \frac{x}{100}\right)^3 = \frac{729}{1000}$

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Taking the cube root:

$1 - \frac{x}{100} = \sqrt[3]{\frac{729}{1000}}$

$1 - \frac{x}{100} = \frac{9}{10}$

$1 - \frac{x}{100} = 0.9$

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Let the value of the item 2 years ago be $V$. The present value is the result of depreciating $V$ for 2 years:

$109350 = V (0.9)^2$

$109350 = V (0.81)$

$V = \frac{109350}{0.81}$

$V = \frac{10935000}{81}$

$V = 135000$

The value of the item 2 years ago was $₹ 135000$.