**Question:**

A car is purchased for Rs 348000. Its value depreciates at 10% per annum during the first year and at 20% per annum during the second year. What will be its value after 2 years?

**Solution:**

Initial value of the car, $P=$ Rs 348000

Rate of depreciation for the first year, $p=10 \%$

Rate of depreciation for the second year, $q=20 \%$

Time, $n=2$ years.

Then the value of the car after two years is given by

Value $=\left\{P \times\left(1-\frac{p}{100}\right) \times\left(1-\frac{q}{100}\right)\right\}$

$=$ Rs. $\left\{348000 \times\left(1-\frac{10}{100}\right) \times\left(1-\frac{20}{100}\right)\right\}$

$=$ Rs. $\left\{348000 \times\left(\frac{100-10}{100}\right) \times\left(\frac{100-20}{100}\right)\right\}$

$=$ Rs. $\left\{348000 \times\left(\frac{90}{100}\right) \times\left(\frac{80}{100}\right)\right\}$

$=$ Rs. $\left\{348000 \times\left(\frac{9}{10}\right) \times\left(\frac{8}{10}\right)\right\}$

$=$ Rs. $(3480 \times 9 \times 8)$

$=$ Rs. 250560

$\therefore$ The value of the car after two years is Rs 250560 .