Question

Due to a rise of \[12\% \] in the price of mangoes a dealer gets 27 kg less for Rs 24750. Find
1) The new price per kg of mangoes.
2) The original price per kg of mangoes (approximately).

Answer 1

Hint:
Here we will firstly assume the price of the original price of the mangoes. Then we will find the value of the new price of the mangoes in terms of the original price of the mangoes. Then by using the given equation we will form an equation and after solving the equation we will get the value of the original price of the mangoes.

Complete Step by step Solution:
Let the original price of the mangoes be \[Rs.\,x\] per Kg.
It is given that there is a rise in the price of the mangoes by \[12\% \]. So the new price of the mangoes becomes
New piece of mangoes \[ = Rs.1.12x\] per Kg
It is given that due to a rise of \[12\% \] in the price of mangoes a dealer gets 27 kg less for Rs 24750. Therefore, we will the equation for the given condition, we get
\[ \Rightarrow \dfrac{{24750}}{{1.12x}} + 27 = \dfrac{{24750}}{x}\]
Now we will solve this equation to get the value of \[x\]. Therefore, we get
\[ \Rightarrow \dfrac{{24750 + 27\left( {1.12x} \right)}}{{1.12x}} = \dfrac{{24750}}{x}\]
\[ \Rightarrow \dfrac{{24750 + 30.2x}}{{1.12x}} = \dfrac{{24750}}{x}\]
On solving the equation further, we get
\[ \Rightarrow 24750 + 30.2x = \dfrac{{24750 \times 1.12x}}{x}\]
\[ \Rightarrow 24750 + 30.2x = 24750 \times 1.12\]
By simply solving the above equation we will get the value of \[x\]. Therefore, we get
\[ \Rightarrow 24750 + 30.2x = 27720\]
\[ \Rightarrow 30.2x = 27720 - 24750 = 2970\]
\[ \Rightarrow x = \dfrac{{2970}}{{30.2}} = 98.21\]
Hence the original price per kg of mangoes is \[Rs.98.21\] per Kg.
Now we will find the value of the new price of the mangoes. Therefore, we get
New price of the mangoes \[ = 1.12\left( {98.21} \right) = Rs.110\]

Hence the new price per kg of mangoes is \[Rs.110\]

Note:
Selling price is the price at which something is sold. Cost price is the cost of producing something or the price at which it is sold without making any money. Profit is the money that you make when you sell something for more than it cost you and loss is the money you make when you sell something for less than it cost you. Discounted amount is the amount when a certain percent of discount is applied to the price of the product. We should know that the discounted amount is always subtracted from the main price of the item.