Question

A vendor bought lemons at the rate of 6 for a rupee. How many for a rupee must he sell to gain \[20\% \]?
A.4 lemons
B.5 lemons
C.6 lemons
D.No lemons

Answer 1

Hint: We will first find the profit earned on selling 6 lemons using the given profit percentage. Then, we will find the selling price of 6 lemons by adding the profit and cost price. Finally, we will find the selling price of one lemon, and then using this we will find the number of lemons that should be sold to earn the given profit percentage.

Formula used:
We will use the following formulas:
1.Profit \[\% = \] (Profit \[ \div \] Cost Price) \[ \times 100\]
2.Profit earned \[ = \] Selling Price \[ - \] Cost Price

Complete step-by-step answer:
It is given that the vendor bought 6 lemons for Re 1. We have to find how many lemons he should sell for Re 1 to gain a profit of \[20\% \].
Here, Cost Price of 6 lemons \[ = {\mathop{\rm Re}\nolimits} 1\]
\[{\rm{Profit}}\% = 20\% \]
Substituting the above values in the formula Profit \[\% = \] (Profit \[ \div \] Cost Price) \[ \times 100\], we get
\[20 = \dfrac{{{\rm{Profit}}}}{1} \times 100\]
Taking 100 to the LHs, we get
\[ \Rightarrow {\rm{Profit}} = \dfrac{{20}}{{100}} = 0.2\]
Thus, the profit to be earned by the vendor on selling 6 lemons is Rs \[0.2\].
Now, we will find the selling price of 6 lemons in order to have a profit of Rs \[0.2\].
Substituting Profit earned \[ = {\rm{Rs}}.0.2\] and Cost Price \[ = {\rm{Re}}1\] in the formula Profit earned \[ = \] Selling Price \[ - \] Cost Price, we get
\[0.2 = \]Selling Price \[ - 1\]
Adding 1 on both side, we get
\[ \Rightarrow \] Selling Price \[ = 1 + 0.2 = {\rm{Rs}}.1.2\]
Therefore, Selling Price of 6 lemons is \[{\rm{Rs}}{\rm{.1}}{\rm{.2}}\]
Now, let us find the selling price of 1 lemon. We do this by dividing \[1.2\] by 6.
Thus, Selling price of 1 lemon \[ = \dfrac{{1.2}}{6} = 0.2\]
Now, the number of lemons to be sold for Re 1 will be obtained by dividing Re. 1 by the selling price of 1 lemon, i.e., Rs. \[0.2\]
Hence, the number of lemons to be sold for Re. 1 \[ = \dfrac{1}{{0.2}} = 5\]
So, the vendor has to sell 5 lemons for Re 1 to gain a profit of \[20\% \], which is option B.
Note: We know that the cost price is defined as the price at which a product is bought. Selling price is the price at which the product is sold. When the selling price is greater than the cost price of the same product, then there will be profit. However, if the selling price is less than the cost price of the same product, then there will be a loss.