In a class test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question.

(a)Radhika got 4 correct answers. If he scored (-12) marks in the competition, how many questions he answered incorrectly?

(b)Sita scored 30 marks, if she has got 10 correct answers, how many questions has she attempted incorrectly

Let's analyze each part of the problem step by step.

### (a) Radhika's Score:

Given:
- **Marks for correct answer:** +5
- **Marks for incorrect answer:** -2
- **Marks for not attempted question:** 0

Radhika got 4 correct answers, so:
- Marks from correct answers = \(4 \times 5 = 20\) marks

Let the number of incorrect answers be \(x\).

Radhika’s total score is given as (-12) marks. So, we can set up the equation as:
\[
\text{Total score} = (\text{Marks from correct answers}) + (\text{Marks from incorrect answers})
\]
\[
-12 = 20 + (-2 \times x)
\]

Now, solve for \(x\):
\[
-12 = 20 - 2x
\]

Subtract 20 from both sides:
\[
-12 - 20 = -2x
\]
\[
-32 = -2x
\]

Divide by -2:
\[
x = \frac{-32}{-2} = 16
\]

So, Radhika answered **16 questions incorrectly**.

### (b) Sita's Score:

Given:
- **Marks for correct answer:** +5
- **Marks for incorrect answer:** -2
- **Marks for not attempted question:** 0

Sita scored 30 marks, and she got 10 correct answers. So:
- Marks from correct answers = \(10 \times 5 = 50\) marks

Let the number of incorrect answers be \(y\).

We can set up the equation as:
\[
\text{Total score} = (\text{Marks from correct answers}) + (\text{Marks from incorrect answers})
\]
\[
30 = 50 + (-2 \times y)
\]

Now, solve for \(y\):
\[
30 = 50 - 2y
\]

Subtract 50 from both sides:
\[
30 - 50 = -2y
\]
\[
-20 = -2y
\]

Divide by -2:
\[
y = \frac{-20}{-2} = 10
\]

So, Sita answered **10 questions incorrectly**.

Would you like to ask for more details or have any questions?

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Here are five related questions that expand on this topic:
1. If Radhika had answered 5 questions correctly, what would her final score be?
2. How many questions would Sita need to answer correctly to achieve a score of 50 marks?
3. If Radhika had answered 2 more questions correctly, how many incorrect answers would she need to get a score of zero?
4. If Sita had scored 40 marks and answered 15 questions correctly, how many questions did she attempt incorrectly?
5. If Radhika’s total score was zero after answering 4 questions correctly, how many questions did she not attempt?

**Tip:** When working with equations, always check your solution by substituting the values back into the original equation to ensure accuracy.

Explore how to solve class test scoring problems with detailed step-by-step solutions for Radhika and Sita's examples. Understand the scoring system where correct answers earn +5 marks, incorrect answers deduct -2 marks, and no attempt gives 0 marks. Suitable for Grades 6-8.

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