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

Answer

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Hint: In this question the percentage of loss can be calculated as \[{\text{Loss% = 100}} \times \dfrac{{{\text{Loss}}}}{{{\text{CP}}}}\]. The vendor gets loss when the cost price is greater than selling price. So, use this concept to reach the solution to the question.

Complete step-by-step answer:

Let selling price of 1 lemon = x

So, selling price (SP) of 45 lemons = 45 x

Given loss = selling price of 3 lemons = 3 x

We know that cost price (CP) = selling price (SP) + loss

= 45 x + 3 x

= 48 x

Consider, \[{\text{Loss% = 100}} \times \dfrac{{{\text{Loss}}}}{{{\text{CP}}}}\]

\[

{\text{Loss% = 100}} \times \dfrac{{3x}}{{48x}} \\

{\text{Loss% = 100}} \times \dfrac{1}{{16}} \\

\therefore {\text{Loss% = 100}} \times 0.625 = 6.25\% \\

\]

Thus, loss percent is 6.25%.

Note: Always remember that cost price (CP) is the amount we pay to buy an item at which it is available. Similarly selling price (SP) is the rate at which an article is sold. There is a profit when the selling price is more than the cost price and there is loss when the cost price is more than the selling price.

Complete step-by-step answer:

Let selling price of 1 lemon = x

So, selling price (SP) of 45 lemons = 45 x

Given loss = selling price of 3 lemons = 3 x

We know that cost price (CP) = selling price (SP) + loss

= 45 x + 3 x

= 48 x

Consider, \[{\text{Loss% = 100}} \times \dfrac{{{\text{Loss}}}}{{{\text{CP}}}}\]

\[

{\text{Loss% = 100}} \times \dfrac{{3x}}{{48x}} \\

{\text{Loss% = 100}} \times \dfrac{1}{{16}} \\

\therefore {\text{Loss% = 100}} \times 0.625 = 6.25\% \\

\]

Thus, loss percent is 6.25%.

Note: Always remember that cost price (CP) is the amount we pay to buy an item at which it is available. Similarly selling price (SP) is the rate at which an article is sold. There is a profit when the selling price is more than the cost price and there is loss when the cost price is more than the selling price.

Last updated date: 28th May 2023

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