Question

An increase of 30% in the price of oranges enables a man to buy 6 kg less for Rs. 300. Find the increased price per kg.
A) 16
B) 15
C) 17
D) 18

Answer 1

 Hint: Cent means hundred and percent simply means a part per hundred, it is a way of expressing amount per hundred. It is denoted by ‘%’
For example, 30 % of ‘x’ means \[\dfrac{{30}}{{100}}x\]
Percentage formula = \[\dfrac{{value}}{{totalvalue}} \times 100\]
Example, if a student gets 15 marks out of 20 then,
Percentage of the marks \[\dfrac{{15}}{{20}} \times 100 = 75\% \]

Complete step-by-step answer:
Given,
The increase in price of the oranges \[ = 30\% \]
Money in hand of the person \[ = Rs.300\]
Let us suppose the initial price of the oranges be X Rs/kg
Then amount of oranges the man can buy initially,
 \[ = \dfrac{{Money{\text{ }}in{\text{ }}hand{\text{ }}of{\text{ }}the{\text{ }}person}}{{the{\text{ }}initial{\text{ }}price{\text{ }}of{\text{ }}the{\text{ }}oranges}} = \dfrac{{300}}{x}\] ----( i )
Now the percentage increase in the price of oranges \[ = 30\% \]
Now the increased price per kg yhat is the new price\[ = \dfrac{{30}}{{100}}x + x = 1.3x\]
Amount of oranges man can buy after the increase in price \[ = \dfrac{{Money{\text{ }}in{\text{ }}hand{\text{ }}of{\text{ }}the{\text{ }}person}}{{The{\text{ final }}price{\text{ }}of{\text{ }}the{\text{ }}oranges}} = \dfrac{{300}}{{1.3x}}\] -----( ii )
To find \[ \to \] the increased price per kg of oranges that is the new price = 1.3 x,
As per the question the man buys 6 kg less than initially,
So the difference between ( i ) and ( ii ) will be equal to 6 kg,
Hence, mathematically
\[\begin{gathered}
   = \dfrac{{300}}{x} - \dfrac{{300}}{{1.3x}} = 6 \\
   \Rightarrow \dfrac{{1.3 - 1}}{{1.3x}} = \dfrac{6}{{300}} \\
   \Rightarrow \dfrac{{0.3}}{{1.3x}} = \dfrac{6}{{300}} \\
  \therefore 1.3x = 15 \\
\end{gathered} \]

Hence the increased price of the oranges per kg is 15 Rupees, which is the required answer.
Thus the answer is option (B)

Note: x% of y = y% of x
 Also in the above question, our assumption of x depends on how we are approaching the question. We could have also assumed the increased price to be x. So don’t confuse one question with multiple ways of solving it.