# 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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