Question

In a test, (+5) marks are given for every correct answer and ( $-2$ ) marks given for every incorrect answer.
(i) Radhika answered all the questions and scored 30 marks though she got the 10 correct answers.
(ii) Jay also answered all the questions and scored ( $-12$ ) marks though he got 4 correct answers.
How many incorrect answers had they attempted?

Answer 1

Hint: First, we have to find total correct marks they got by using the formula i.e. total marks for correct answer = marks for correct answer $\times $ number of correct answers. Then subtracting those marks from the total mark they got which will be marks of incorrect answers. After that, on dividing it with marks given for every negative answer, we get the total number of incorrect answers the have attempted i.e. total marks for incorrect answer = marks for incorrect answer $\times $ number of incorrect answers.

Complete step-by-step answer:

Here, we are given positive marks every correct answer and negative marks for every incorrect answer i.e. for the correct answer $=+5$ and for every incorrect answer $=-2$ marks.
Case1: Radhika got total marks $=30$ , correct answer $=10$
So, the total marks for correct answer = marks for correct answer $\times $ number of correct answers.
Total marks for correct answer $=5\times 10=50$
Thus, Radhika got a total 50 marks for 10 correct answers.
Now, subtracting total marks she got from total marks of correct answer we will get marks for incorrect answer. So, writing as
$=50-30=20$ marks.
So, she got 20 marks for the incorrect answer. Now, we know that for every incorrect answer $=-2$ marks.
So, the total marks for incorrect answer = marks for incorrect answer $\times $ number of incorrect answers
Substituting values, we get
$20=-2\times $ number of incorrect answers
So, dividing by $-2$ on both sides, we get
Number of incorrect answers $=-10$
So, the number of incorrect answers are 10 (we can ignore minus sign here because the question cannot be in negative value).
Case2: Jay got total marks $=-12$ , correct answer $=4$
So, the total marks for correct answer = marks for correct answer $\times $ number of correct answers.
Total marks for correct answer $=5\times 4=20$
Thus, Jay got a total 20 marks for 4 correct answers.
Now, subtracting total marks he got from total marks of correct answer we will get marks for incorrect answer. So, writing as
$=20-\left( -12 \right)=20+12=32$ marks.
So, he got 32 marks for incorrect answers. Now, we know that for every incorrect answer $=-2$ marks.
So, the total marks for incorrect answer = marks for incorrect answer $\times $ number of incorrect answers
Substituting values, we get
$32=-2\times $ number of incorrect answers
So, dividing by $-2$ on both sides, we get
Number of incorrect answers $=-16$
So, the number of incorrect answers are 16 (we can ignore minus sign here because the question cannot be in negative value).
Hence, Radhika and Jay got 10 and 16 questions incorrect, respectively.

Note: Be careful while writing the final answer. Sometimes mistakes happen by taking $-16$ and $-10$ as the final incorrect answer which is wrong. Also, after finding the total correct marks we can directly use the formula i.e. Total marks=Total correct marks +total incorrect marks
So, solving for Radhika we get
$30=50+\left( -2 \right)\times $ total incorrect answers
On solving we get,
$30-50=\left( -2 \right)\times $ total incorrect answers
$-20=\left( -2 \right)\times $ total incorrect answers
Thus, on solving we get positive +10 incorrect answers. Thus, the answer remains the same except minus sign.