Question

The value of a car decreases annually by $ 20\% $ . If the present value of the car be $ Rs.4,50,000 $ . What will be its value after $ 2 $ years?

Answer 1

Hint: For solving this question, we will calculate the car value after two years by using the formula $ {\text{Present value}} \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] $ . And by substituting the values we will get to the answer.
Formula used:
Value after the specified year,
 $ {\text{Present value}} \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] $
Here,
 $ d $ , will be the decrease in the value.

Complete step by step solution:
First of all, we will see the values given in the question. So we have the present value which is being given $ Rs.4,50,000 $ .
Also, there is a decrease in the value annually which is denoted by $ d $ and is equal to $ 20\% $
Therefore, the value after the $ 2 $ years will be calculated as-
By using the formula which is $ {\text{Present value}} \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] \times \left[ {\dfrac{{\left( {100 - d} \right)}}{{100}}} \right] $ and substituting the values, we get
 $ \Rightarrow 4,50,000 \times \left[ {\dfrac{{\left( {100 - 20} \right)}}{{100}}} \right] \times \left[ {\dfrac{{\left( {100 - 20} \right)}}{{100}}} \right] $
And on solving the small braces of the equation, we get
 \[ \Rightarrow 4,50,000 \times \left[ {\dfrac{{80}}{{100}}} \right] \times \left[ {\dfrac{{80}}{{100}}} \right] \]
Now solving the braces, we get
 \[ \Rightarrow 4,50,000 \times \left[ {\dfrac{4}{5}} \right] \times \left[ {\dfrac{4}{5}} \right] \]
On multiplying the above equation, we get
 \[ \Rightarrow Rs.4,50,000 \times \dfrac{{16}}{{25}}\]
Now solving the division and multiplication of the above solution, we get
 $ \Rightarrow Rs.2,88,000 $
Therefore, the value after $ 2 $ years will be $ Rs.2,88,000 $ .

Note: We can also solve it by using another formula. So for this, the formula will be $ P{\text{resent value - }}\dfrac{d}{{100}} \times {\text{ Present value}} $ . By using this we will have two values for each year. And in the end, on adding it we have the value after the certain required year. Since we can see from the solution that the only important thing in this question is the formula and if we know it we can solve it easily. In this type of question, we have to be careful while writing the numbers as one zero can change the complete scenario of the problem.