Question

A washing machine was purchased 3 years ago for Rs. 19,440. It’s value depreciates at $16\dfrac{2}{3}\% $ per annum. Calculate its present value and value after 1 year.
A) Rs. 11250 ; Rs. 9375
B) Rs. 9375 ; Rs. 11250
C) Rs. 13500 ; Rs. 7812
D) Rs. 7812 ; Rs. 13500

Answer 1

Hint: We can calculate the present value by depreciating the given percentage each year, the price of the preceding month will become CP (cost price) for the next year.
Similarly, the value of next year can be obtained by depreciating (given percentage) from the current price.
The price for each year can be calculated as:
Price = CP – D% X CP where D% is the percentage of depreciation and CP is cost price.

Complete step-by-step answer:
Cost of washing machine 3 years ago (CP) = Rs. 19,400
Depreciation rate per annum (D%)= $16\dfrac{2}{3}\% $
= $\dfrac{{50}}{{3 \times 100}}$ [In mixed fractions]
To find the value of present cost, we need to calculate the depreciated values for the 3 years after purchasing the machine:
Price after 1 year of purchase
= 19400 - $\dfrac{{50}}{{3 \times 100}} \times 19400$ [CP – D% X CP]
= 19400 – 3240
= Rs. 16200
🡪This becomes CP for the next year.
Price after 2 years of purchase
= 16200 - $\dfrac{{50}}{{3 \times 100}} \times 16200$ [CP – D% X CP]
= 16200 – 2700
= Rs. 13500
🡪This becomes CP for the next year.
Price after 3 years of purchase
= 13500 - $\dfrac{{50}}{{3 \times 100}} \times 13500$ [CP – D% X CP]
= 13500 – 2250
= Rs. 11250
As this is the value after three years of purchase, it is the current price of the machine.
The value after 1 year will also be depreciated, therefore, it can be given as:
11250 - $\dfrac{{50}}{{3 \times 100}} \times 11250$ [CP – D% X CP]
= 11250 – 1875
= Rs. 9375
Therefore, the current value and the value after 1 year of the given washing machine is Rs. 11250 and Rs. 9375
 So, the correct answer is “Option A”.

Note: Always convert decreasing or increasing percentage into mixed fraction if given in improper fraction. This can be done as:
$a\dfrac{b}{c} = \dfrac{{c \times a + b}}{c}$