Question

Sonu had purchased a bicycle three years back. It’s value decreased to Rs.1728 at the rate of 20% per annum. For what amount had sonu purchased the bicycle?

Answer 1

Hint: Assume ‘x’ as the amount in which sonu purchased the bicycle. Calculate the value of the bicycle after one year by subtracting 20% of x from x. Now, calculate the value of the bicycle after two years by subtracting 20% of the obtained value from the same obtained value. Finally, calculate the value of the bicycle after the third year by subtracting 20% of the amount after two years from the same amount after two years and equate it with Rs.1728. Solve for the value of x to get the answer.

Complete step-by-step solution
Here, we have been given the information that the cost of a bicycle purchased by Sonu decreases to Rs.1728 at the rate of 20% per annum. We have to find the value of the original price of the bicycle.
Now, let us assume the original price of the bicycle was x. It is given that after one year is reduced by 20%, so we have,
Price of the bicycle after 1 year = x – 20% of x
Price of the bicycle after 1 year = x - \[\left( \dfrac{20}{100} \right)x\]
Price of the bicycle after 1 year = \[\dfrac{4x}{5}\]
Now, after second years the price is again reduced by 20%, so we have,
Price of the bicycle after 2 years = \[\dfrac{4x}{5}\] - 20% of \[\dfrac{4x}{5}\]
Price of the bicycle after 2 years = \[\dfrac{4x}{5}-\left( \dfrac{20}{100} \right)\left( \dfrac{4x}{5} \right)\]
Price of the bicycle after 2 years = \[\dfrac{16x}{25}\]
Finally, it is given to us that after third year the price is again reduced by 20%, so we have,
Price of the bicycle after 3 years = \[\dfrac{16x}{25}\] - 20% of \[\dfrac{16x}{25}\]
Price of the bicycle after 3 years = \[\dfrac{16x}{25}-\left( \dfrac{20}{100} \right)\left( \dfrac{16x}{25} \right)\]
Price of the bicycle after 3 years = \[\dfrac{64x}{125}\]
Here, we have been given that after 3 years the rate of cycle is Rs.1728, so equating this value with the obtained expression of the price above, we get,
\[\begin{align}
  & \Rightarrow \dfrac{64x}{125}=1728 \\
 & \Rightarrow x=\dfrac{1728\times 125}{64} \\
\end{align}\]
\[\Rightarrow \] x = Rs.3375
Hence, the price of the bicycle three years ago was Rs.3375.

Note: One must understand the language of the question and should not get confused in it. Here, after every year the price of the cycle is getting reduced on the newly formed price and not on the original one. So, we have to calculate 20% of the reduced price and not the original price ‘x’ after the first and second year. Remember that this question cannot be solved by a simple interest or compound interest formula.