Question

Plz ans ques 4 its really urgent

Answer 1

Question :-

In a competitive examination, one mark is awarded for each correct answer while ½ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many answers did she answer correctly ?

Answer :-

Number of correctly answered questions are 100.

Solution :-

Number of questions answered by Jayanti = 120

Let the number questions correctly answered be x

Number of questions wrongly answered = Number of questions answered by Jayanti - Number questions correctly answered = (120 - x)

Mark awared for correcly answered questions = 1 mark

Mark deducted for wrongly answered questions = ½ marks

Marks awarded to Jayanti for correctly answered questions = 1(x) = 'x' marks

Marks deducted to Jayanti for wrongly answered questions = ½ (120 - x) = ½(120) - ½(x) = 120/2 - x/2 = (60 - x/2) marks

Marks scored by Jayanti = 90

⇒ Marks awarded to Jayanti for correctly answered questions - Marks deducted to Jayanti for wronly answered questions = 90

$\bf \implies x - (60 - \dfrac{x}{2}) = 90$

$\bf \implies x - 60 + \dfrac{x}{2} = 90$

$\bf \implies x + \dfrac{x}{2} = 90 + 60$

$\bf \implies x + \dfrac{x}{2} =150$

$\bf \implies \dfrac{x}{1} + \dfrac{x}{2} =150$

Taking LCM

$\bf \implies \dfrac{x(2)}{1(2)} + \dfrac{x}{2} =150$

$\bf \implies \dfrac{2x}{2} + \dfrac{x}{2} =150$

$\bf \implies \dfrac{2x + x}{2} =150$

$\bf \implies \dfrac{3x}{2} =150$

$\bf \implies 3x =150 \times 2$

$\bf \implies x = \dfrac{150 \times 2}{3}$

$\bf \implies x = 50 \times 2$

$\bf \implies x = 100$

Therefore number of correctly answered questions are 100.