Question

By selling $45$ lemons, a vendor loses a sum equal to the selling price of $3$ lemons. Find his loss percent?

Answer 1

Hint: For solving this particular question , we will use the concept of Cost price and Selling price , for solving this we must know Loss $ = $ Cost Price $ - $ Selling Price ( loss is equals to the difference of cost price and the selling price) .

Complete step by step solution:
We know that loss is equals to the difference of cost price and the selling price ,
Mathematically , we can write this as ,
Loss $ = $ Cost Price $ - $ Selling Price ,
According to the question ,
Loss $ = $ Cost Price of $45$ lemons $ - $ Selling Price of $45$ lemons,
We can say that ,
Selling price of $3$ lemons = Cost Price of $45$ lemons $ - $ Selling Price of $45$ lemons,
Or
Cost Price of $45$ lemons = Selling Price of $45$ lemons $ + $ Selling price of $3$ lemons ,
$ \Rightarrow $ Cost Price of $45$ lemons = Selling Price of $48$ lemons.
Now, let the Cost Price of $1$ lemon be rs $x$ .
Then, The Cost Price of $48$ lemons will be rs $48x$ .
And we already know that ,
The Selling Price of $48$ lemons is equal to the Cost Price of $45$ lemons that is rs $45x$ .
Thus , the Cost Price of $48$lemons is greater than the Selling Price of $48$ lemons.
Therefore, there is a loss.
And it is given as ,
 loss $ = $ Cost Price of $48$ lemons $ - $ Selling Price of $48$ lemons ,
$ = $ rs $(48x - 45x)$
$ = $ rs $(3x)$
Loss $\% = \left( {\dfrac{{loss}}{{CP}} \times 100} \right)\% $
$
= \left( {\dfrac{{3x}}{{48x}} \times 100} \right)\% \\
 = 6.25\% \\
 $
Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. For solving this type of question, we have to consider that loss is equals to the difference of cost price and the selling price , and Loss $\% = \left( {\dfrac{{loss}}{{CP}} \times 100} \right)\% $ .