In an examination, there are five subjects and each has the same maximum. A boy’s marks are in the ratio 3 : 4 : 5 : 6 : 7and his aggregate is `(3)/(5)` th of the full marks. In how many subjects did he get more than `50%` marks ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the given information
We know that a boy's marks in five subjects are in the ratio of 3:4:5:6:7, and his total marks are \( \frac{3}{5} \) of the full marks.

### Step 2: Define the full marks
Assume the maximum marks for each subject is 100. Therefore, the total full marks for five subjects is:
\[ \text{Total Full Marks} = 5 \times 100 = 500 \]

### Step 3: Calculate the boy's total marks
The boy's total marks are \( \frac{3}{5} \) of the total full marks:
\[ \text{Boy's Total Marks} = \frac{3}{5} \times 500 = 300 \]

### Step 4: Express the marks in terms of a variable
Let the marks in each subject be represented as:
- Subject 1: \( 3x \)
- Subject 2: \( 4x \)
- Subject 3: \( 5x \)
- Subject 4: \( 6x \)
- Subject 5: \( 7x \)

### Step 5: Set up the equation for total marks
Now, we can set up the equation for the total marks:
\[ 3x + 4x + 5x + 6x + 7x = 300 \]
Combining the terms gives:
\[ 25x = 300 \]

### Step 6: Solve for \( x \)
To find \( x \), divide both sides by 25:
\[ x = \frac{300}{25} = 12 \]

### Step 7: Calculate the marks in each subject
Now, we can calculate the marks obtained in each subject:
- Subject 1: \( 3x = 3 \times 12 = 36 \)
- Subject 2: \( 4x = 4 \times 12 = 48 \)
- Subject 3: \( 5x = 5 \times 12 = 60 \)
- Subject 4: \( 6x = 6 \times 12 = 72 \)
- Subject 5: \( 7x = 7 \times 12 = 84 \)

### Step 8: Determine which subjects have more than 50% marks
Since the maximum marks for each subject is 100, 50% of the marks is 50. Now, we check each subject:
- Subject 1: 36 (not more than 50)
- Subject 2: 48 (not more than 50)
- Subject 3: 60 (more than 50)
- Subject 4: 72 (more than 50)
- Subject 5: 84 (more than 50)

### Step 9: Count the subjects with more than 50% marks
The subjects where the boy scored more than 50% are:
- Subject 3
- Subject 4
- Subject 5

Thus, the number of subjects in which he scored more than 50% marks is **3**.

### Final Answer
The boy got more than 50% marks in **3 subjects**.

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