Nidhi gave BA exams. Maximum marks of arts, social science, home science and history are 75,90,120 & 135 respectively. If she obtained 56%, 73%, 102 marks and 78% respectively. Find her overall percentage ?

Options

A. 0.75
B. `74.66%`
C. `71(3)/(7)%`
D. `73.22%`

Answer

To find Nidhi's overall percentage in her BA exams, we will follow these steps:

### Step 1: Calculate the Marks Obtained in Each Subject
1. **Arts**: Maximum marks = 75, Percentage = 56%
\[ \text{Marks obtained} = \left(\frac{56}{100} \times 75\right) = 42 \]

2. **Social Science**: Maximum marks = 90, Percentage = 73%
\[ \text{Marks obtained} = \left(\frac{73}{100} \times 90\right) = 65.7 \]

3. **Home Science**: Maximum marks = 120, Marks obtained = 102 (given directly).

4. **History**: Maximum marks = 135, Percentage = 78%
\[ \text{Marks obtained} = \left(\frac{78}{100} \times 135\right) = 105.3 \]

### Step 2: Calculate Total Marks Obtained
Now, we will sum up all the marks obtained:
\[ \text{Total Marks Obtained} = 42 + 65.7 + 102 + 105.3 = 315 \]

### Step 3: Calculate Total Maximum Marks
Next, we will sum up the maximum marks for all subjects:
\[ \text{Total Maximum Marks} = 75 + 90 + 120 + 135 = 420 \]

### Step 4: Calculate Overall Percentage
Finally, we calculate the overall percentage:
\[ \text{Overall Percentage} = \left(\frac{\text{Total Marks Obtained}}{\text{Total Maximum Marks}} \times 100\right) = \left(\frac{315}{420} \times 100\right) \]
Calculating this gives:
\[ \text{Overall Percentage} = \left(\frac{315}{420}\right) \times 100 = 75\% \]

### Final Answer
Nidhi's overall percentage is **75%**.

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