In a test consisting of 140 questions, a candidate correctly answered 70% of the first 80 questions. What percentage of the remaining questions does the candidate need to correctly answerto score 60% in the test?

Options

A. 0.4
B. `45(1)/3%`
C. `46(2)/3%`
D. `35%`

Answer

To solve the problem step-by-step, we can follow these instructions:

### Step 1: Calculate the number of questions answered correctly from the first 80 questions.
The candidate answered 70% of the first 80 questions correctly.

\[ \text{Correct answers from first 80 questions} = 70\% \text{ of } 80 = \frac{70}{100} \times 80 = 56 \]

### Step 2: Determine the total number of questions and the required score for 60%.
The total number of questions in the test is 140. To score 60% in the test:

\[ \text{Required score} = 60\% \text{ of } 140 = \frac{60}{100} \times 140 = 84 \]

### Step 3: Calculate the number of correct answers needed from the remaining questions.
The candidate has already answered 56 questions correctly from the first 80. Therefore, the number of correct answers needed from the remaining questions is:

\[ \text{Correct answers needed} = 84 - 56 = 28 \]

### Step 4: Determine how many questions are left to answer.
The total number of questions is 140, and the candidate has already answered 80 questions. Thus, the number of remaining questions is:

\[ \text{Remaining questions} = 140 - 80 = 60 \]

### Step 5: Calculate the percentage of remaining questions that need to be answered correctly.
Let \( x \) be the percentage of the remaining 60 questions that need to be answered correctly. The number of correct answers from the remaining questions can be expressed as:

\[ \text{Correct answers from remaining questions} = \frac{x}{100} \times 60 \]

Setting this equal to the number of correct answers needed:

\[ \frac{x}{100} \times 60 = 28 \]

### Step 6: Solve for \( x \).
To find \( x \), rearranging the equation gives:

\[ x \times 60 = 2800 \]

Dividing both sides by 60:

\[ x = \frac{2800}{60} = \frac{280}{6} = 46.67 \]

### Step 7: Convert to percentage.
Thus, the percentage of the remaining questions that the candidate needs to answer correctly is:

\[ x = 46 \frac{2}{3} \% \]

### Final Answer:
The candidate needs to correctly answer approximately **46.67%** of the remaining questions to score 60% in the test.

---