Question

A fruit seller bought \[80{\text{ }}kg\] of apples at \[Rs.{\text{ }}12.50{\text{ }}per{\text{ }}kg.\] He sold \[50{\text{ }}kg\] of it at a loss of \[10\% .\] At what price per kg should he sell the remaining apples so as to gain \[20\% .\] on the whole?
A) \[Rs.{\text{ }}32.75\]
B) \[Rs.{\text{ }}21.25\]
C) \[Rs.{\text{ }}18.26\]
D) \[Rs.15.24\]

Answer 1

Hint: Here, it is a problem of profit and loss. If profit is there, the selling price increases or more than the cost price and when loss happens, the selling price is less than the cost price. Basic formula is SP = CP + Profit [SP=Selling Price].

Complete step-by-step answer:
Given, a fruit seller bought \[80{\text{ }}kg\] of apples at \[Rs.{\text{ }}12.50{\text{ }}per{\text{ }}kg.\]
So, Total cost price of apples= Total weight of apples X cost of apples per kg
Now putting the values in the formula we get,
Total cost price of apples $ = 80 \times 12.50 = Rs.1000/ - $
Fruit seller sold 50 kg of the apples at a loss of 10%
$\therefore $cost price of 50 kg apples= Total weight of apples X cost of apples per kg
$\therefore $cost price of 50 kg apples $ = 50 \times 12.50 = Rs.625/ - $
Now, Selling price of 50 kg apples sold were\[ = cost{\text{ }}price{\text{ }}of{\text{ }}50{\text{ }}kg{\text{ }}apples - (cost{\text{ }}price{\text{ }}of{\text{ }}50{\text{ }}kg{\text{ }}apples \times loss\% )\]
Now putting the values in the formula we get ,
  $ = 625 - 625 \times \dfrac{{10}}{{100}} = Rs.562.50$
Now, He has to gain 20% on the whole, we use formula as,
\[ \Rightarrow Total{\text{ }}selling{\text{ }}price{\text{ }}of{\text{ }}apples = Total{\text{ }}cost{\text{ }}price{\text{ }}of{\text{ }}apples \times profit\% + Total{\text{ }}cost{\text{ }}price{\text{ }}of{\text{ }}apple{s_{}}\]
Now putting the values in the formula we get the amount he has to gain is
$ = 1000 \times \dfrac{{20}}{{100}} + 1000$
By solving the equation we get,
 $ = 200 + 1000$
$ = 1200$
Remaining balance he has earn = \[Total{\text{ }}selling{\text{ }}price{\text{ }}of{\text{ }}apples - Selling{\text{ }}price{\text{ }}of{\text{ }}50{\text{ }}kg{\text{ }}apples\]
Now we put the values, we get
$ = Rs.\left( {1200 - 562.5} \right) = Rs.637.50$
$\therefore $Price of apples per kg $ = \dfrac{{637.50}}{{30}}$
[$\because $\[80 - 50{\text{ }} = {\text{ }}30{\text{ }}kg\]\[80 - 50{\text{ }} = {\text{ }}30{\text{ }}kg\] of apples are left]
$ = Rs.21.25$
The seller should sell the apples at a cost of $Rs.21.25$ to gain the profit of $20\% $

Hence, the correct option is (B).

Note: Selling Price: the price at which the article is sold.
Cost Price: The price at which the articles are bought.
Profit: It is the difference between the amount earned and the amount spent in buying any article.
Loss: It is the difference between the amount spent and the amount earned in buying any article.