Ex.1.4 Q6 Integers Solution - NCERT Maths Class 7

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Question

In a class test \((+3)\) marks are given for every correct answer and \((–2)\) marks are given for every incorrect answer and no mark for not attempting any question.

i) Radhika scored \(20\) marks. If she has got \(12\) correct answers, how many questions has she attempted incorrectly?

ii) Mohini scores \(–5\) marks in this test, though she has got \(7\) correct answers. How many questions has she attempted incorrectly?

 

Text Solution

   

Steps:

Given: –

Marks given for every correct answer \(=3\) marks

Marks given for every incorrect answer\( =–2\)

Marks for not attempting any question  \(=0\)

i)Total score of Radhika \(= 20\) marks

 No. of correct answers given by Radhika \(=12 \) answers

\[\begin{align} \text{Marks obtained for correct answers}&=\text{ 3  }\!\!\times\!\!\text{  12 } \\  &= \text{36 marks}  \end{align}\]

\(\begin{align}\text{Marks obtained for incorrect answers}& =\text{Total score} - \text{Marks obtained}\\& \qquad \qquad \qquad \quad \text{for 12 correct answers} \\ & =2036 \\ & =16\,\text{marks} \end{align}\)

Marks obtained for every incorrect answer \( =–2 \) marks

\[\begin{align}\text{Thus, number of incorrect answers}&=\text{ -16  }\!\!\div\!\!\text{  }\left( \text{-2} \right) \\  &=\text{ 8}\end{align}\]

Therefore, she attempted \(8\) questions wrongly.

ii) Total score of Mohini \(=–5\)

No. of correct answers given by Mohini \(=7\)

\[\begin{align} \text{Marks obtained for correct answers}&=\text{7  }\!\!\times\!\!\text{  3 } \\  & = \text{21}\,\text{marks}  \end{align}\]

\(\begin{align}\text{Marks obtained for incorrect answers}&=\text{ Total score} - \text{Marks obtained}\\& \qquad \qquad \qquad \quad \;\;\text{for correct answers} \\ & =\,-5\,- 21 \\ & =-26\end{align}\)

Marks obtained for every incorrect answer\(= –2\) marks

Thus, number of incorrect answers\(= (–26) ÷ (–2) = 13\)

Therefore, she attempted \(13\) questions wrongly.

  
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