Question

A fruit seller loses 10% by selling 26 oranges at Rs.25. how many oranges should he sell for Rs.5 to gain 17 per cent?

Answer 1

Hint: The original price of an item or the cost to make the item is called cost price and is represented by CP. The price at which the item is sold by the seller to the buyer is called selling price and is represented by SP. Use this concept along with the knowledge of loss and profit to find out the number of oranges that should be sold.

Complete step-by-step answer:
In this question, we are given that a fruit seller sells 26 oranges for Rs.25 and losses 10% in this process.
The selling price of 26 oranges $ = Rs.25 $
The selling price of 1 orange $ = Rs.\dfrac{{25}}{{26}} $
We, know that $ loss = cost\,price - selling\,price $
That is
 $
  L = CP - SP \\
   \Rightarrow CP = SP + L \;
  $
Also, $ CP = \dfrac{{SP \times 100}}{{100 - {L_\% }}} $
Therefore, $ CP = \dfrac{{\dfrac{{25}}{{26}} \times 100}}{{100 - 10}} = \dfrac{{25 \times 100}}{{26 \times 90}} = \dfrac{{125}}{{117}} $
Thus we find the cost price of each orange.
Now, we have to find how many oranges should be sold for Rs.5 to gain a profit of 17%.
The selling price of one orange to get a profit of 17% should be,
 $
  SP = \dfrac{{CP \times (100 + gai{n_\% })}}{{100}} \\
  SP = \dfrac{{\dfrac{{125}}{{117}} \times (100 + 17)}}{{100}} = \dfrac{{125}}{{100}} = \dfrac{5}{4} \;
  $
Let n be the number of oranges sold for Rs.5
We have, selling price of 1 orange to get a profit of 17% $ = Rs.\dfrac{5}{4} $
 $
  number\,of\,oranges = \dfrac{{total\,selling\,price}}{{selling\,price\,of\,one\,orange}} \\
\Rightarrow n = \dfrac{5}{{\dfrac{5}{4}}} = 5 \times \dfrac{4}{5} = 4 \;
  $
Hence, the fruit seller should sell 4 oranges for Rs.5 to gain a profit of 17%.
So, the correct answer is “4”.

Note: If the selling price is greater than the cost price then we say that the seller has made a profit on the item, and the profit is calculated by subtracting the cost price from the selling price. But if the cost price is greater than the selling price then we say that the seller has suffered a loss on the item, and the loss is calculated by subtracting the selling price from the cost price.