Question

The price of an article is first decreased by \[20\% \] and then increased by \[30\% \]. If the resulting price is \[Rs.{\text{ }}416\], the original price of the article is
A) \[Rs.{\text{ }}350\]
B) \[Rs.{\text{ }}405\]
C) \[Rs.{\text{ }}400\]
D) \[RS.{\text{ }}450\]

Answer 1

Hint:We will assume the original price as \[Rs{\text{ }}100\] or \[Rs{\text{ }}x.\] Then calculate decrease or increase per cent as per the question and would compare the given current price to the resultant price. Convert word statements in the form of the mathematical expressions and find the correlation between the known and unknown in the equations. Remember, there will be an addition when the rate of change in percentage is increased and subtraction when the rate of change in percentage is decreased.

Complete step-by -step solution:
According to the question, An article is first decreased by\[20\% \]and then increased by \[30\% \]now it results in \[Rs.{\text{ }}416\].
Let us consider that the original price of the article be $x$
Case1: The decrease in price is given as 20%.
The price drop is calculated as:
$
  {P_d} = \dfrac{x}{{\left( {\dfrac{{100}}{{20}}} \right)}} \\
   = \dfrac{x}{5} \\
 $ \[\]
The new price will be: $x - \dfrac{x}{5} = \dfrac{{4x}}{5}$
Case 2: Increase in price is given as 30%.
The price increase is calculated as:
$
  {P_i} = \left( {\dfrac{{30}}{{100}}} \right)\dfrac{{4x}}{5} \\
   = \dfrac{{6x}}{{25}} \\
 $
The new price will be: $\dfrac{{4x}}{5} + \dfrac{{6x}}{{25}} = \dfrac{{20x + 6x}}{{25}} = \dfrac{{26x}}{{25}} - - - - (i)$
Now according to the given statement, the resultant price is $416$.
So, equation (i) to 416 we get,
$
 \Rightarrow \dfrac{{26x}}{{25}} = 416 \\
  x = \dfrac{{416 \times 25}}{{26}} \\
   = 400 \\
 $
 Therefore, the original price of the article is Rs. 400.

Hence the correct answer is option C

Note: In these types of problems we need to be very careful about what percent is increased or decreased and from which quantity. Also, we should assume proper unknown values which should relate the maximum part or values of the solution.