Question

12 The present price of a machine is 15,463. If its value depreciates every year by 6%, then find its
before two years.​

Answer 1

$\sf{ \pink{ \large{Given:}}}$

⇰ Present price of a machine = Rs. 15,463

⇰ Rate of depreciation ( every year ) = 6%

$\sf{ \pink{ \large{To \: Find:}}}$

✠ Value before two years.

$\sf{ \pink{ \large{Solution}}}$

Let the value of a machine 2 years before be x.

Now, we know that its value depreciates every year by 6%

So, value of machine after first year

$\sf= x - \dfrac{6}{100} x \\ \\ \sf = \dfrac{100x - 6x}{100} \\ \\ \sf = \dfrac{94x}{100} \\ \\ \sf = 0.94x$

Now, value of machine after second year

For finding the value after second year we will substitute the value of x, as

Value of machine after second year

$\sf = 0.94x - \dfrac{6}{100} (0.94x) \\ \\ \sf = 0.94x - \dfrac{6}{100} \times 0.94x \\ \\ \sf = 0.94x - \dfrac{5.64}{100}x \\ \\ \sf = \dfrac{94x - 5.64x}{100} \\ \\ \sf = \dfrac{88.36}{100}x \\ \\ \sf = 0.8836x$

We know present value of machine is Rs. 15,463, which is value after two years. By this value we will find value before two years.

$\sf0.8836x = 15463 \\ \\ \sf x = \dfrac{15463}{0.8836} \\ \\ \sf x = 17500$

∴ The value of machine before two years = $\green{ \underline{ \boxed{ \sf{Rs.17500}}}}$

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