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A machine depreciates in value each year at the rate of $10 %$ of its previous value. However, every second year there is some maintenance work, so that in that particular year depreciation is only $5 %$ of its previous value. If at the end of the fourth year the value of the machine stands at Rs. $146205$ , then find the value of the machine at the start of the first year?

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Rs.

190000

Rs.

200000

Rs.

195000

Rs.

210000

answer is B.

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Detailed Solution

It is given that value of machine at end of fourth year is

Rs . 146205

and it depreciate at rate of

10 %

. And every second-year depreciation is only

5 % .

Let the value of the machine, at the onset, be

Rs . x

.
Here we shall apply the rule,
Final value

=

original value

\times {(1 + rate)}^{time}

.
Here the rate will be negative since the value is depreciating.
For two yrs. the rate of depreciation is

10 %

∴

The value after

2

years

=

x \times {(1 - \frac{10}{100})}^{2}

\Rightarrow

Value after 2 years

= x \times \frac{9}{10} \times \frac{9}{10}

The rate of depreciation for next

2

yrs

= 5 %

∴

The value after next

2

years,

\Rightarrow

Value after next 2 years

=

x \times \frac{9}{10} \times \frac{9}{10} \times {(1 - \frac{5}{100})}^{2}

\Rightarrow

Value after next 2 years

= x \times \frac{9}{10} \times \frac{9}{10} \times \frac{19}{20} \times \frac{19}{20}

But the final value after

4

years

=

Rs.

146205

∴ x \times \frac{9}{10} \times \frac{9}{10} \times \frac{19}{20} \times \frac{19}{20} = 146205

\Rightarrow x = \frac{146205 \times 40000}{81 \times 19 \times 19}

\Rightarrow x = 5 \times 40000

\Rightarrow x =

Rs.

200000

So,

4

years. back, the value of the machine was Rs.

200000

.
Hence, the correct option is 2.

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