question_answer 29)

In a class test \[(+3)\] marks are given for every correct answer and (?2) marks are given for every incorrect answer and no marks 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?                

Answer:

                (i) Let \['x'\] be the number of incorrect question attempted by Radhika. According to the question, we get \[\text{(}+\text{3)}\times \text{12}+x\times (-\text{ 2})=\text{2}0\] \[\Rightarrow \]               \[\text{36}-\text{2}x=\text{2}0\] \[\Rightarrow \]         \[\text{2}x=\text{36}-\text{2}0\] \[\Rightarrow \]               \[x=\frac{16}{2}=8\] Therefore, Radhika attempted 8 incorrect questions. (ii) Let \['x'\] be the number of incorrect question attempted by Mohini. According to the question, we get \[\text{(}+\text{3)}\times \text{7}+x\times (-\text{ 2})=-\text{ 5}\] \[\Rightarrow \]               \[~\text{21}-\text{2}x=-\text{5}\] \[\Rightarrow \]         \[\text{2}x=\text{21}+\text{5}\] \[\Rightarrow \]               \[x=\frac{26}{2}=13\] Therefore, Mohini attempted 13 incorrect questions.