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.