Question

A fruit seller bought 75kg apples at Rs. 30 per kgs. He sold one third of apples at a loss of $5\mathrm{\%}$ At what rate should he sell the remaining, so that his overall gain is $10\mathrm{\%}.$

Answer 1

Hint- Here in this question since the seller has sold some apples with some loss already, therefore to compensate or to make overall profit of $$10\mathrm{\%}$$ as required in this question we need to add the loss of sold products to the selling price of remaining apples . So first we will calculate the cost price and then proceed accordingly.

Complete step-by-step solution -
Given that the cost price of 1 kg apples is Rs 30
He sold the ${\displaystyle \frac{1}{3}}rd$ of the apples at a loss of $5\mathrm{\%}$
Therefore selling price of the ${\displaystyle \frac{1}{3}}rd$ apples is
Since the cost price of 25kg apples is $=25\times 30=Rs.750$
Selling price of 25kg at loss of $5\mathrm{\%}$ is
$$\begin{gathered} \text{loss = }{\displaystyle \frac{\text{cost price - selling price}}{\text{cost price}}}\times 100 \\ 5={\displaystyle \frac{750-\text{selling price}}{750}}\times 100 \\ {\displaystyle \frac{5\times 750}{100}}=750-\text{selling price} \\ \text{selling price = 750 - 37}\text{.5} \\ \text{selling price = Rs}\text{. 712}\text{.5} \end{gathered}$$
The total cost price of the 75kg apples is
$$\begin{gathered} =75\times Rs.30 \\ =Rs.2250 \end{gathered}$$
Now on the total cost price, he has to gain $10\mathrm{\%}$
Therefore,
Profit = $2250\times {\displaystyle \frac{10}{100}}=Rs.225$
Now the selling price of the 75kg would be = profit + cost price
= Rs. 225 + Rs. 2250
= Rs. 2475
The cost already sold by the seller is Rs. 712.5
Remaining price would be =
$$\begin{gathered} =Rs.2475-Rs.712.5 \\ =Rs.1762.5 \end{gathered}$$
Now the seller has to sell 50 kg of apples at Rs. 1762.5 to gain $10\mathrm{\%}$
So, the selling price of per kg apple is
$$\begin{gathered} ={\displaystyle \frac{1762.5}{50}} \\ =Rs32.25 \end{gathered}$$.

Note- In order to solve questions related to profit and loss, the first step is to read the question carefully and understand the terms such as profit, gains, loss, marked price, cost price and more. Learn the formula of profit and loss and try to solve the question step by step. Follow the unitary method to solve the questions such as calculate the cost of a single item then the whole set of items etc.