Mrs. Shakya is a wholesaler. She has bought 15 similar cartons of
cooking oil from a dealer, each carton containing 12 bottles of ait. When
she reached her shop and opened the cartoon, she found that 5 bottes
were broken and not fit for sale.
(a) Write the formula to find the loss percent.
(b) She sold each of the remaining bottles of oil for Rs 824 and made
. What was her cost prioe?
© How much less or more than Rs 400 strould she sell each bottle

Question

Mrs. Shakya is a wholesaler. She has bought 15 similar cartons of
cooking oil from a dealer, each carton containing 12 bottles of ait. When
she reached her shop and opened the cartoon, she found that 5 bottes
were broken and not fit for sale.
(a) Write the formula to find the loss percent.
(b) She sold each of the remaining bottles of oil for Rs 824 and made

. What was her cost prioe?
© How much less or more than Rs 400 strould she sell each bottle

UpStudy AI · Accepted Answer

**(a)**  
Let the total cost price be $$ T $$ and the cost of the unsellable (broken) bottles be $$ L $$. Then the loss percent is given by  
$$
\text{Loss percent} = \frac{L}{T} \times 100.
$$  
In this problem the loss occurs because some bottles are broken. If the cost per bottle is $$ x $$, then the cost of the broken bottles is $$ 5x $$ and the total cost is $$ 15\times12x = 180x $$. In that case,  
$$
\text{Loss percent} = \frac{5x}{180x} \times 100 = \frac{5}{180}\times 100.
$$

**(b)**  
Let the cost price per bottle be $$ x $$. Although Mrs. Shakya bought 180 bottles, 5 bottles were broken. Thus, the sale is made on 175 bottles. However, the overall cost is still based on 180 bottles, i.e., the total cost is  
$$
180x.
$$  
The total selling price is  
$$
175 \times 824.
$$  
Given that she made an overall profit of $$ 10\% $$, we have  
$$
\frac{\text{Total Selling Price} - \text{Total Cost}}{\text{Total Cost}} \times 100 = 10.
$$
Substituting,  
$$
\frac{175\cdot824 - 180x}{180x} \times 100 = 10.
$$
It is simpler to work with the fraction without the factor $$ 100 $$, so write  
$$
\frac{175\cdot824 - 180x}{180x} = 0.1.
$$
First, compute  
$$
175 \cdot 824 = 175\times800 + 175\times24 = 140000 + 4200 = 144200.
$$
Now solve for $$ x $$:  
$$
\frac{144200 - 180x}{180x} = 0.1 \quad \Longrightarrow \quad 144200 - 180x = 0.1 \times 180x.
$$
Since $$ 0.1 \times 180x = 18x $$, the equation becomes  
$$
144200 - 180x = 18x.
$$
Combine like terms:  
$$
144200 = 180x + 18x = 198x.
$$
Thus,  
$$
x = \frac{144200}{198}.
$$
Simplify by dividing numerator and denominator by 2:  
$$
x = \frac{72100}{99}.
$$
This is the exact cost price per bottle. In decimal form,  
$$
x \approx \frac{72100}{99} \approx 728.28.
$$
So her cost price per bottle is approximately Rs $$728.28$$.

**(c)**  
Mrs. Shakya sold each bottle for Rs $$824$$. We are asked how much less or more than Rs $$400$$ this selling price is. The difference is  
$$
824 - 400 = 424.
$$
Since $$824$$ is greater than $$400$$, she sold each bottle for Rs $$424$$ more than Rs $$400$$.
**(a)** The loss percent is calculated as $$ \frac{5x}{180x} \times 100 = \frac{5}{180} \times 100 $$. **(b)** Mrs. Shakya's cost price per bottle is approximately Rs $$728.28$$. **(c)** She sold each bottle for Rs $$424$$ more than Rs $$400$$.

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