Question

A man bought bananas at the rate of 10 for 45 dollars and sold at the rate of one dozen bananas for 51 dollars. Find his gain or loss percent.

Answer 1

Hint:
Here we will find the cost price and selling price of one item by using the unitary method. We will then compare the cost price and selling price of one item to find whether he incurred profit or loss. We will use a loss/profit percentage formula to find the required value.

Formula Used:
We will use the following formulas:
1. \[{\rm{Loss}}\% = \dfrac{{{\rm{Loss}}}}{{CP}} \times 100\], where, \[CP\] is the cost price at which the man bought is, \[SP\] is selling price at which the man sold it
2. \[{\rm{Loss}} = CP - SP\]

Complete step by step solution:
It is given that the man bought 10 bananas for 45 dollars, so
Cost Price of 10 bananas \[ = \$ 45\]
Now we will use the unitary method to find the Cost Price of 1 banana. Therefore, we get
Cost Price of 1 banana \[ = \dfrac{{45}}{{10}} = \$ 4.5\]
Now, the man sells the 12 bananas for 51 dollars.
Selling Price of 12 bananas \[ = \$ 51\]
Again, we will use the unitary method to find Selling Price of 1 banana. Therefore, we get
$\therefore $ Selling Price of 1 banana \[ = \dfrac{{51}}{{12}} = \$ 4.25\]
As, we can see that the selling price of one banana is less than the cost price of one banana that means the man suffers a loss. So, we will find the loss of the man on one banana.
Substituting \[CP = 4.5\] and \[SP = 4.25\] in the formula \[{\rm{Loss}} = CP - SP\], we get
\[{\rm{Loss}} = 4.5 - 4.25\]
Subtracting the terms, we get
\[ \Rightarrow {\rm{Loss}} = \$ 0.25\]
Now, we will find the loss percentage.
Substituting \[{\rm{Loss}} = \$ 0.25\] and \[CP = 4.5\] in the formula \[{\rm{Loss}}\% = \dfrac{{{\rm{Loss}}}}{{CP}} \times 100\], we get
Loss% \[ \Rightarrow {\rm{Loss}}\% = \dfrac{{0.25}}{{4.5}} \times 100\]
Multiply the numerator, we get
\[ \Rightarrow {\rm{Loss}}\% = \dfrac{{25}}{{4.5}}\]
Dividing the terms, we get
\[ \Rightarrow {\rm{Loss}}\% = 5.55\% \]

So, that means the man suffered a loss of \[5.55\% \].

Note:
We know that the cost price is the price at which a product is purchased. Selling price is the price at which the product is sold. A seller incurs profit when the selling price is greater than the cost price of the product. A seller incurs loss when the selling price is greater than the cost price of the product. We can find profit by subtracting the selling price from the cost price. In any question, first, we find the cost price and selling price for the same amount of things and that is usually done by finding the cost of one item. We will then use it to calculate the loss or profit percentage.