Question

# The present cost of a mobile phone is Rs. 15000. If its value decreases every year by 5 %, find the cost of the mobile 2 years ago.

Hint: Assign the cost of the mobile before two years to a variable. The value of the mobile decreases by 5 % every year. Hence, find the equation relating the variable to the present cost and find the answer.

We need to determine the cost of the mobile before two years.

Let the cost of the mobile two years ago be x.

The value of the mobile decreases by 5 % every year. Then, before one year the value of the mobile would have decreased by 5 % of x and the actual value one year ago is x – (5 % of x).

Value of mobile one year ago = $x - \left( {\dfrac{5}{{100}} \times {\text{ }}x} \right)$

Value of mobile one year ago = ${\text{ }}x - 0.05{\text{ }}x$

Value of mobile one year ago = ${\text{ 0}}{\text{.95 }}x$

Hence, the value of mobile before one year is 0.95 x.

The present value of mobile would have decreased by 5 % from the previous years, that is, 0.95 x.

The decrease in the value of mobile is 5 % of 0.95 x. The present value of mobile is 0.95 – (5 % of 0.95 x).

Present value of mobile = ${\text{0}}{\text{.95 }}x - \left( {\dfrac{5}{{100}} \times 0.95x} \right)$

Present value of mobile = ${\text{ 0}}{\text{.95 }}x - \left( {0.05 \times 0.95x} \right)$

Present value of mobile = ${\text{ 0}}{\text{.95 }}x - 0.0475x$

Present value of mobile = ${\text{0}}{\text{.9}}025x$

It is given that the present value of the mobile is Rs. 15,000. Hence, equating 0.9025x to 15000, we have:

$0.9025x = 15000$

Solving for x, we have:

$x = \dfrac{{15000}}{{0.9025}}$

$x = 16620.50$

Hence, the value of the mobile before two years is Rs. 16620.50

Note: The question asks to find the value of the mobile, two years ago, meaning, two years before. You might make a mistake and calculate the value after two years, which is wrong.