Question

A fruit seller bought $80kg$ of apples at ₹ $12.50$ per kg. He sold $50$ kg of it at a loss of $10$ per cent. At what price per kg should he sell the remaining apples so as to gain $20$ per cent on the whole?
(A) ₹ $12.25$
(B) ₹ $15.25$
(C) ₹ $19.25$
(D) ₹ $21.25$

Answer 1

Hint: Calculate the cost price of 50 kg of apples. Then calculate the loss accrued using percentage.

Complete step by step solution:
It is given that , A fruit seller bought $80\,kg $ of apples at ₹ $12.50$ per kg.
After that he sold $50$ kg of it at a loss of $10$ per cent.
So, we are asked to calculate at what price per kg should he sell the remaining apple so as to gain $20$ per cent on the whole.
According to question,
$ $Cost of $1\,kg$ apple= ₹ $12.50$
So, Cost of $50\,kg$ apple = ₹ $12.50 \times 50$
So, Cost of $50\,kg$ apple = ₹ $625$
Now loss on $50$ kg apples $ = 10\% .$
Let the selling price on $50\,kg$ be $'x'.$
Then using formula to get $'x'$
$\dfrac{{C.P - S.P}}{{C.P}} \times 100 = $Loss % on $50\,kg$
Putting values in formula.
$ \Rightarrow \dfrac{{625 - x}}{{625}} \times 100 = 10$
$625 - x = \dfrac{{10 \times 258}}{4}$
$625 - x = \dfrac{{125}}{2} = 62.5$
$x = - 62.5 + 625$
$\therefore x = 562.5$ ₹
Selling price on \[50kg\] to loss $10\% $
Now for remaining $30kg$ apple out of $80\,kg.$
Cost price of $1\,kg$ apple$ = 12.50$ ₹
Cost price of $30\,kg $ apple $ = 12.50 \times 30$
$ = 375$ ₹
Let selling price of $30\,kg$ apple be $y$
So, Total cost price of $30\,kg$ apple=$625 + 375$ ₹
$ = $₹ $1000$
And total selling price of $80\,kg$ apple$ = $₹ $562.5 + y$
Hence the required profit on the whole$\% = $(Total selling price-Total cost price)×100/(Total Cost Price) = gain % on $80\,kg.$
Then put value in this formula
$ \Rightarrow \dfrac{{562.5 + y - 1000}}{{1000}} \times 100 = 20$
$562.5 + y - 1000 = 200$
$y = 1200 - 562.5$
$y = 637.5$ ₹
So, the selling price of $30kg\, Apple = y $
$ = 637.5$ ₹

Selling price of $ 1kg $ Apple $ = \dfrac{{637.5}}{{30}}$
$= ₹ 21.25 $ .

Note:
We need to understand that he was at a loss for the sale of the first 50 kg apples. So he needed to recover that loss and the new profit, both, from the sale of remaining 30 kg apples. So, the total investment and the total profit must have been taken out from the sale of the remaining 30 kg apples.