In a test consisting of 120 questions, a candidate correctly answer 60% of the first 90 question. What percentage of the remaining questions does he need to answer correctly so that his answer to 55% of the total questions in the test are correct?

Options

A. 36
B. 45
C. 42
D. 40

Answer

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

### Step 1: Calculate the number of questions answered correctly from the first 90 questions.
The candidate answered 60% of the first 90 questions correctly.

\[ \text{Correct answers from the first 90 questions} = 60\% \text{ of } 90 = \frac{60}{100} \times 90 = 54 \]

### Step 2: Determine the total number of questions in the test.
The total number of questions in the test is given as 120.

### Step 3: Calculate the total number of correct answers needed to achieve 55% of the total questions.
To find out how many questions need to be answered correctly to achieve 55% of the total questions:

\[ \text{Total correct answers needed} = 55\% \text{ of } 120 = \frac{55}{100} \times 120 = 66 \]

### Step 4: Calculate the number of correct answers needed from the remaining questions.
The candidate has already answered 54 questions correctly. Therefore, the number of additional correct answers needed from the remaining questions is:

\[ \text{Additional correct answers needed} = 66 - 54 = 12 \]

### Step 5: Determine the number of remaining questions.
The total number of questions is 120, and the candidate has already answered 90 questions. Thus, the remaining questions are:

\[ \text{Remaining questions} = 120 - 90 = 30 \]

### Step 6: Calculate the percentage of remaining questions that need to be answered correctly.
To find the percentage of the remaining 30 questions that must be answered correctly to achieve 12 additional correct answers:

\[ \text{Percentage needed} = \left(\frac{\text{Correct answers needed}}{\text{Remaining questions}}\right) \times 100 = \left(\frac{12}{30}\right) \times 100 = 40\% \]

### Final Answer:
The candidate needs to answer **40%** of the remaining questions correctly.

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