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The value of a machine depreciates at the rate of 25% each year. If the difference between its values at the end of the third and the fourth year is Rs.17,199, then what is the value of the machine at the end of the first year?

The value of a machine depreciates at the rate of 25% each year. If the difference between its values at the end of the third and the fourth year is Rs.17,199, then what is the value of the machine at the end of the first year? Correct Answer Rs. 1,22,304

Given:

Rate of depreciation = 25%

3rd year value - 4th year value = Rs. 17,199

Formula used:

Depreciated value after 'n' years = pn

Calculation:

Let the present value be 'p'

∵ 3rd year value - 4th year value = Rs. 17,199

⇒ p3 - p4 = 17,199

⇒ p3 - p4 = 17,199

⇒ p(3/4)3 - p(3/4)4 = 17,199

⇒ 27p/64 - 81p/256 = 17,199

⇒ (108p - 81p)/256 = 17,199

⇒ 27p/256 = 17,199

⇒ p = (17,199 × 256)/27

⇒ p = 637 × 256

⇒ p = 1,63,072

∴ Value of machine after 1 year = 1,63,0721

= 1,63,072

= 1,63,072(3/4)

= Rs. 1,22,304

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