Question

The cost of a car goes down every year by 20% of its previous value. Find its original cost if the cost of it after 2 years is Rs 5,65,000.?

Answer 1

Cost of a car at the end of 2 years = Rs 5,65,000
The cost decreases every year by 20%
Let the cost at the beginning of $1^{st}$ year be 100.
At the beginning of $2^{nd}$ year it will be Rs 80 (i.e. 100 - 20% of 100)

At the beginning of $3^{rd}year=Rs64(80-20\%of80)$
Thus, a car that cost Rs 100 will cost 64 at the beginning of third year.
The cost of a car is Rs 5,65,000 after 2 years
Let the original cost be Rs x
Therefore, 64 : 100 : : 5,65,000 : x
Since the product of extremes is equal to the product of means
$64\times x=5,65,000\times 100$
$x=\frac{56500000}{64}$
$x=882812.5$
Therefore, the original cost of the car was Rs 8,82,812.5.