Question

The selling price of 16 spoons is equal to the cost price of 15 spoons. Find the loss percent.

Answer 1

Hint: In the given question, we have been given that the cost price of 15 spoons is the same as that of the selling price of 16 spoons, which means the merchant is incurring a loss of 1 spoon per transaction. For solving this, we are going to assume the cost price and selling price of the spoons. We are going to take it a constant (as it is easy to comprehend and solve) as the cost price and the selling price (preferably the LCM of 15 and 16 as it is divisible by both and does not result in a fraction), then we are going to find the cost price and selling price of one spoon and apply the formula to find the loss percent.
Formula Used:
We are going to use the formula of loss percent, which is:
 $$\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}={\displaystyle \frac{\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}-\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}}}\times 100$$

Complete step-by-step answer:
In this question we are going to assume the cost/selling price of the items. We take the LCM of the number of items for convenience and it makes no difference in the final answer.
Now, the LCM of 15 and 16 is 240.
So, the assumed cost price of 15 spoons or the selling price of 16 spoons is 240.
CP of 15 spoons is $$=240$$
CP of 1 spoon is $$={\displaystyle \frac{240}{15}}=16$$
SP of 16 spoons is $$=240$$
SP of 1 spoon is $$={\displaystyle \frac{240}{16}}=15$$
Now, loss percent $$={\displaystyle \frac{CP-SP}{CP}}\times 100$$
Hence, loss percent $$={\displaystyle \frac{16-15}{16}}\times 100={\displaystyle \frac{1}{16}}\times 100=6.25\mathrm{\%}$$
Hence, the loss percent is $$6.25\mathrm{\%}$$ .
So, the correct answer is “$$6.25\mathrm{\%}$$ ”.

Note: So, we saw that in solving questions like these, it is best to take the assumed cost price and the selling price a constant (we take the constant as the LCM of the cost price and the selling price, since it is the LCM, it does not leave any fraction and hence, it does not create confusion). Then we just divide the constant by the number of items in the two prices and find the loss or gain percent by applying their respective formula and we are going to have our answer.