Sanjay scored 75 out of 150 marks in his mid-term exam and 105 out of 150 in his annual exam. The percentage increase in his marks is:

Options

A. `30%`
B. `45%`
C. `50%`
D. `40%`

Answer

To find the percentage increase in Sanjay's marks from his mid-term exam to his annual exam, we can follow these steps:

### Step 1: Calculate the percentage of marks in the mid-term exam.
Sanjay scored 75 out of 150 marks in his mid-term exam.

\[ \text{Percentage in mid-term} = \left( \frac{\text{Marks scored}}{\text{Total marks}} \right) \times 100 \]

\[ \text{Percentage in mid-term} = \left( \frac{75}{150} \right) \times 100 \]

\[ = 0.5 \times 100 = 50\% \]

### Step 2: Calculate the percentage of marks in the annual exam.
Sanjay scored 105 out of 150 marks in his annual exam.

\[ \text{Percentage in annual exam} = \left( \frac{105}{150} \right) \times 100 \]

\[ = 0.7 \times 100 = 70\% \]

### Step 3: Calculate the increase in percentage.
To find the increase in percentage, we subtract the mid-term percentage from the annual percentage.

\[ \text{Increase in percentage} = \text{Percentage in annual exam} - \text{Percentage in mid-term} \]

\[ = 70\% - 50\% = 20\% \]

### Step 4: Calculate the percentage increase.
Now, we calculate the percentage increase based on the initial percentage (mid-term percentage).

\[ \text{Percentage increase} = \left( \frac{\text{Increase in percentage}}{\text{Initial percentage}} \right) \times 100 \]

\[ = \left( \frac{20}{50} \right) \times 100 \]

\[ = 0.4 \times 100 = 40\% \]

### Final Answer:
The percentage increase in Sanjay's marks is **40%**.

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