(C) Let $x$ be the number of correct answers and $(120-x)$ be the number of wrong answers.According to the problem,the total marks obtained is $90$.Th

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(C) Let $x$ be the number of correct answers and $(120-x)$ be the number of wrong answers.According to the problem,the total marks obtained is $90$.The equation is: $x \times 1 - (120 - x) \times \frac{1}{2} = 90$.Expanding the equation: $x - 60 + \frac{x}{2} = 90$.Adding $60$ to both sides: $x + \frac{x}{2} = 150$.Combining terms: $\frac{3x}{2} = 150$.Solving for $x$: $x = \frac{150 \times 2}{3} = 100$.Therefore,Jayanti answered $100$ questions correctly.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

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In a competitive examination,one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly?

A
$50$
B
$75$
C
$100$
D
$155$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

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For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

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In a competitive examination,one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly?

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In a two-digit number,the digit at the unit's place is $3x$ and the digit at the ten's place is $2x$. Then,that number is $\ldots \ldots \ldots \ldots$

Solve the following pair of linear equations by the substitution and cross-multiplication methods:$8x + 5y = 9$$3x + 2y = 4$

For a pair of equations,if $a_{1} b_{2}-a_{2} b_{1}=0, b_{1} c_{2}-b_{2} c_{1}=0$ and $c_{1} a_{2}-c_{2} a_{1}=0$,then the solution set of the pair of equations is ...........

The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

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Solve the following pair of linear equations by the substitution and cross-multiplication methods:
$8x + 5y = 9$
$3x + 2y = 4$