Question

The value of a car which was purchased 3 years ago depreciates at 20% per annum. If its present value is rupees 89600 for how much was it purchased? Also find the total depreciation.

Answer 1

$<B>Solution:$

Let purchase value of car = Rs. x

Rate = 20% per annum

Present value of car = Rs. 89,600

Time = 3 years

Now, find amount:

$A = P(1 - { \frac{R}{100} })^{n}$

$= > 89,600 = x(1 - { \frac{20}{100} })^{3}$

$= > 89,600 = x( \frac{4}{5} )^{3}$

$= > 89,600 = \frac{64}{125} x$

$= > \frac{89,600 \times 125}{64} = x$

$= > x = 1,75,000$

Thus , the car was purchased for Rs. 1,75,000

Total depreciation

= Rs. 1,75.000 - Rs. 89,600

= Rs. 85,400

$<B>[ANSWER: Rs. 85,400]$

Answer 2

Let purchase value of car = Rs. x

Rate = 20% per annum

Present value of car = Rs. 89,600

Time = 3 years

Now, find amount:

A = P(1 - { $\frac{R}{100} })^{n}$

A=P(1− 100

R

)

n

= > 89,600 = x(1 - { \frac{20}{100} })^{3}=>89,600=x(1− 100×20 ) 3

= > 89,600 = x($\frac{4}{5} )^{3}$

=>89,600=x(54 ) 3

= > 89,600 = $\frac{64}{125}$ x=>89,600= 125 64

x

= >$\frac{89,600 \times 125}{64}$= x=>

64

89,600×125

=x

= > x = 1,75,000=>x=1,75,000

Thus , the car was purchased for Rs. 1,75,000

Total depreciation

= Rs. 1,75.000 - Rs. 89,600

= Rs. 85,400

[ANSWER: Rs. 85,400]