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The cost of a Microwave depreciates by Rs. 630 during the second year and by Rs. 567 during the third year. Calculate :

i) The rate of  depreciation per annum.

ii) The original cost of the machine.


1. 10%, Rs.7500
2. 20%, Rs.8000
3. 20%, Rs.8500
4. 10%, Rs.7000

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Best answer
Correct Answer - Option 4 : 10%, Rs.7000

Given

During the 2nd year, Rs. 630 depreciates from the cost of Microwave and Rs.567 during the 3rd year.

Formula Used

V = P0[ 1 +r /100]n

Calculation∶

Let the original cost of the Microwave be Rs. P and the rate of depreciation of its value be r% p.a. then, the value of the microwave(in Rs.) after one year, two years and 3 years or

P(1 - r/100), p(1 - r/100)2 and P (1 - r/100)3 respectively.

 

Given that the cost of the machine depreciations by Rs.630 during the second year and by Rs.567 during the third year,

P[ 1 - r/100] - P [ 1 - r/100]2 = 630

⇒ P (1 - r/100] - P[1 - r/100]2 = 630

⇒ P (1 - r/100) × r/100 = 720      (1)

Also, P[ 1 - r/100]2 - P[ 1- r/100]3 = 567

⇒ P[1 - r/100]2 × r/100 = 567      (2)

Divide eq.(2) by eq.(1), we get

1 - r/100 = 567/630 = 9/10

⇒ r/100 = 1/10

⇒ r = 10 %

Thus, the rate of depreciation = 10% p.a.

ii) Putting r = 10 in eq. (1), we get

⇒ P(1 - 1/10) × 1/10 = 630

⇒ P × 9/100 = 630

⇒ P = 7000.

∴ The original cost of Microwave is Rs. 7000.

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