
A woman buys toffees at \[Rs\text{ }2.50\] a dozen and an equal number at \[Rs.3\] a score. She sells them at \[Rs\text{ 3}.60\]a score and thus makes a profit of \[Rs\text{ }10\]. How many toffees did she buy?
A $10000$
B $12000$
C $5000$
D $6000$
Answer
483.3k+ views
Hint:
Here we need to apply the concept of conversions from one unit to another unit and Profit formula.
Conversions Required: One score equals $20$ objects.
One dozen equals $20$ objects.
Formula Required: $Profit=Selling\text{ }\Pr ice\text{-}\operatorname{Cos}t\text{ }\Pr ice$
Profit incurs when selling Price is more than cost price.
We need to find how many toffees she buys.
Complete step by step solution:
Let the number of toffee bought in each case is\[x\] .
Total toffees bought is \[2x\].
Cost of \[12\] toffees is \[Rs\text{ }2.50\]
$\Rightarrow $ Cost of \[1\] toffees is \[Rs\text{ }\dfrac{2.50}{12}\]
Cost of \[x\] toffees bought in first case is \[Rs\text{ }x\times \left( \dfrac{2.50}{12} \right)\]
Cost of $20$ toffees bought in first case is \[Rs.3\]
$\Rightarrow $Cost of \[1\] toffees is \[Rs\text{ }\dfrac{3}{20}\]
Cost of \[x\] toffees bought in second case is \[Rs\text{ }x\times \left( \dfrac{3}{20} \right)\]
Total cost price of \[2x\] toffees is \[Rs\text{ }x\times \left( \dfrac{2.50}{12} \right)+Rs\text{ }x\times \left( \dfrac{3}{20} \right)\]
According to the question,
Selling Price of $20$ toffees is \[Rs\text{ 3}.60\]
Selling Price of \[1\] toffees is \[Rs\text{ }\dfrac{\text{3}.60}{20}\]
Total Selling price of \[2x\] toffees is \[Rs\text{ 2}x\times \left( \dfrac{3.60}{20} \right)\]
Profit is \[Rs\text{ }10\]
$\Rightarrow $ Total Selling price of \[2x\] toffees- Total cost price of \[2x\] toffees is \[Rs\text{ }10\]
$\begin{align}
& \Rightarrow \text{2}x\times \left( \dfrac{3.60}{20} \right)-\left( x\times \left( \dfrac{2.50}{12} \right)+\text{ }x\times \left( \dfrac{3}{20} \right) \right)=10 \\
& \Rightarrow \text{2}x\times \left( \dfrac{3.60}{20} \right)-x\left( \dfrac{25}{120}+\dfrac{3}{20} \right)=10 \\
& \Rightarrow \dfrac{9x}{25}-\dfrac{43x}{120}=10 \\
& \Rightarrow \dfrac{216x-215x}{600}=10 \\
& \Rightarrow \dfrac{x}{600}=10 \\
& \Rightarrow x=6000 \\
\end{align}$
Total toffees bought is \[2x\],
\[\begin{align}
& \Rightarrow 2x=2\times 6000 \\
& =12000 \\
\end{align}\]
Therefore, the total toffees she bought is $12000$ .
Hence, Option choice B is the correct answer.
Note:
In such types of questions the concept of conversions from one unit to another unit and Profit formula is needed. Assigning the variable to the unknown and equations are framed as per the relation in the question, then solved to get the required value.
Here we need to apply the concept of conversions from one unit to another unit and Profit formula.
Conversions Required: One score equals $20$ objects.
One dozen equals $20$ objects.
Formula Required: $Profit=Selling\text{ }\Pr ice\text{-}\operatorname{Cos}t\text{ }\Pr ice$
Profit incurs when selling Price is more than cost price.
We need to find how many toffees she buys.
Complete step by step solution:
Let the number of toffee bought in each case is\[x\] .
Total toffees bought is \[2x\].
Cost of \[12\] toffees is \[Rs\text{ }2.50\]
$\Rightarrow $ Cost of \[1\] toffees is \[Rs\text{ }\dfrac{2.50}{12}\]
Cost of \[x\] toffees bought in first case is \[Rs\text{ }x\times \left( \dfrac{2.50}{12} \right)\]
Cost of $20$ toffees bought in first case is \[Rs.3\]
$\Rightarrow $Cost of \[1\] toffees is \[Rs\text{ }\dfrac{3}{20}\]
Cost of \[x\] toffees bought in second case is \[Rs\text{ }x\times \left( \dfrac{3}{20} \right)\]
Total cost price of \[2x\] toffees is \[Rs\text{ }x\times \left( \dfrac{2.50}{12} \right)+Rs\text{ }x\times \left( \dfrac{3}{20} \right)\]
According to the question,
Selling Price of $20$ toffees is \[Rs\text{ 3}.60\]
Selling Price of \[1\] toffees is \[Rs\text{ }\dfrac{\text{3}.60}{20}\]
Total Selling price of \[2x\] toffees is \[Rs\text{ 2}x\times \left( \dfrac{3.60}{20} \right)\]
Profit is \[Rs\text{ }10\]
$\Rightarrow $ Total Selling price of \[2x\] toffees- Total cost price of \[2x\] toffees is \[Rs\text{ }10\]
$\begin{align}
& \Rightarrow \text{2}x\times \left( \dfrac{3.60}{20} \right)-\left( x\times \left( \dfrac{2.50}{12} \right)+\text{ }x\times \left( \dfrac{3}{20} \right) \right)=10 \\
& \Rightarrow \text{2}x\times \left( \dfrac{3.60}{20} \right)-x\left( \dfrac{25}{120}+\dfrac{3}{20} \right)=10 \\
& \Rightarrow \dfrac{9x}{25}-\dfrac{43x}{120}=10 \\
& \Rightarrow \dfrac{216x-215x}{600}=10 \\
& \Rightarrow \dfrac{x}{600}=10 \\
& \Rightarrow x=6000 \\
\end{align}$
Total toffees bought is \[2x\],
\[\begin{align}
& \Rightarrow 2x=2\times 6000 \\
& =12000 \\
\end{align}\]
Therefore, the total toffees she bought is $12000$ .
Hence, Option choice B is the correct answer.
Note:
In such types of questions the concept of conversions from one unit to another unit and Profit formula is needed. Assigning the variable to the unknown and equations are framed as per the relation in the question, then solved to get the required value.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
When people say No pun intended what does that mea class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which king started the organization of the Kumbh fair class 8 social science CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Advantages and disadvantages of science
