Daya gets pocket money from his father every day. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3.00 on second day, Rs 3.25 on third day and so on. Find:
the amount saved by Daya on `30^(th)` day

Answer

To find the amount saved by Daya on the 30th day, we can observe that the amounts saved each day form an arithmetic progression (AP).

### Step-by-step Solution:

1. **Identify the first term (a) and the common difference (d)**:
- The amount saved on the first day is Rs 2.75.
- The amount saved on the second day is Rs 3.00.
- The amount saved on the third day is Rs 3.25.
- Thus, the first term \( a = 2.75 \).
- The common difference \( d \) can be calculated as:
\[ d = 3.00 - 2.75 = 0.25 \]

2. **Use the formula for the nth term of an arithmetic progression**:
- The formula for the nth term \( a_n \) of an AP is given by:
\[ a_n = a + (n - 1) \cdot d \]
- Here, we need to find the amount saved on the 30th day, so \( n = 30 \).

3. **Substitute the values into the formula**:
- Plugging in the values:
\[ a_{30} = 2.75 + (30 - 1) \cdot 0.25 \]
- Simplifying this:
\[ a_{30} = 2.75 + 29 \cdot 0.25 \]

4. **Calculate \( 29 \cdot 0.25 \)**:
- \( 29 \cdot 0.25 = 7.25 \)

5. **Add this to the first term**:
- Now, we can calculate:
\[ a_{30} = 2.75 + 7.25 = 10.00 \]

6. **Conclusion**:
- Therefore, the amount saved by Daya on the 30th day is Rs 10.00.

### Final Answer:
Daya saves Rs 10.00 on the 30th day.

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