# Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

${\text{A}}{\text{.}}$ 20 Questions

${\text{B}}{\text{.}}$ 40 Questions

${\text{C}}{\text{.}}$ 50 Questions

${\text{D}}{\text{.}}$ 15 Questions

Last updated date: 15th Mar 2023

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Answer

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Hint – try to solve these questions with the help of linear equations and compare them both.

Complete step-by-step solution -

According to the question, let the right answer be $x$ and the number of wrong questions as $y$

Now as per the question,

$

\Rightarrow 3x - y = 40....\left( i \right) \\

\Rightarrow 4x - 2y = 50....\left( {ii} \right) \\

$

Now multiplying $\left( i \right)$ by $\left( {2} \right)$ and subtracting $\left( {ii} \right)$ from $\left( i \right)$ will get,

$

\Rightarrow 6x - 2y - 4x + 2y = 80 - 50 \\

\Rightarrow 2x = 30 \\

\Rightarrow x = 15 \\

$

Now putting in $x$ in $\left( i \right)$ will get,

$

\Rightarrow 3 \times 15 - y = 40 \\

\Rightarrow 45 - y = 40 \\

\Rightarrow - y = 40 - 45 \\

$

Now cancelling out the same signs we will get,

$y = 5$

So correct answer $ = 15$, wrong answer $ = 5$

Total question $ = x + y = 15 + 5 = 20 $ questions

So, the option “A” is correct.

Note- Use of linear equations in solving such questions will be helpful. In mathematics, a linear equation is an equation that may be put in the form where the variables are, and are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.

Complete step-by-step solution -

According to the question, let the right answer be $x$ and the number of wrong questions as $y$

Now as per the question,

$

\Rightarrow 3x - y = 40....\left( i \right) \\

\Rightarrow 4x - 2y = 50....\left( {ii} \right) \\

$

Now multiplying $\left( i \right)$ by $\left( {2} \right)$ and subtracting $\left( {ii} \right)$ from $\left( i \right)$ will get,

$

\Rightarrow 6x - 2y - 4x + 2y = 80 - 50 \\

\Rightarrow 2x = 30 \\

\Rightarrow x = 15 \\

$

Now putting in $x$ in $\left( i \right)$ will get,

$

\Rightarrow 3 \times 15 - y = 40 \\

\Rightarrow 45 - y = 40 \\

\Rightarrow - y = 40 - 45 \\

$

Now cancelling out the same signs we will get,

$y = 5$

So correct answer $ = 15$, wrong answer $ = 5$

Total question $ = x + y = 15 + 5 = 20 $ questions

So, the option “A” is correct.

Note- Use of linear equations in solving such questions will be helpful. In mathematics, a linear equation is an equation that may be put in the form where the variables are, and are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.

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