Answer
Verified
388.2k+ 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
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE