# 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

Answer

Verified

361.2k+ views

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.

Last updated date: 26th Sep 2023

•

Total views: 361.2k

•

Views today: 9.61k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

The poet says Beauty is heard in Can you hear beauty class 6 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE