let's calculate how long it will take for the price of the motorbike to reach Rs. 1,86,624.
In the first year, the price decreases by 10%, which means it becomes 90% of the original price: Rs. 3,60,000 * 0.9 = Rs. 3,24,000.
In the second year, the price decreases again by 10%, so it becomes 90% of Rs. 3,24,000: Rs. 3,24,000 * 0.9 = Rs. 2,91,600.
After the first two years, the motorbike depreciates at a rate of 20% each year.
We'll set up an equation to solve for the time it takes for the price to reach Rs. 1,86,624:
Rs. 2,91,600 * (1 - 0.2)^t = Rs. 1,86,624
Simplifying the equation:
0.8^t = 1,86,624 / 2,91,600
0.8^t = 0.64
Taking the logarithm of both sides:
t * log(0.8) = log(0.64)
t = log(0.64) / log(0.8)
Using a calculator, we find that t is approximately 3.6547.
So, it will take approximately 3.6547 years for the price of the motorbike to reach Rs. 1,86,624 from the beginning.
Or 4 rounded up