Rajeev read `3/8` part of a book in one day. Next day he read `4/5` part of the rest. Now 30 pages are left to read. How many pages are there in the book?

Options

A. 360
B. 120
C. 240
D. 380

Explanation

To find the total number of pages in the book, we can follow these steps:

1. **Let the total number of pages in the book be \( x \)**.

2. **Calculate the pages read on the first day**:
- Rajeev reads \( \frac{3}{8} \) of the book on the first day.
- Pages read on the first day = \( \frac{3}{8} \times x \).

3. **Calculate the remaining pages after the first day**:
- Remaining pages = Total pages - Pages read on the first day
- Remaining pages = \( x - \frac{3}{8}x = \frac{5}{8}x \).

4. **Calculate the pages read on the second day**:
- Rajeev reads \( \frac{4}{5} \) of the remaining pages on the second day.
- Pages read on the second day = \( \frac{4}{5} \times \frac{5}{8}x = \frac{4}{8}x = \frac{1}{2}x \).

5. **Calculate the remaining pages after the second day**:
- Remaining pages = Remaining pages after first day - Pages read on the second day
- Remaining pages = \( \frac{5}{8}x - \frac{1}{2}x \).
- To subtract these fractions, convert \( \frac{1}{2} \) to eighths: \( \frac{1}{2} = \frac{4}{8} \).
- Remaining pages = \( \frac{5}{8}x - \frac{4}{8}x = \frac{1}{8}x \).

6. **Set up the equation based on the information given**:
- We know that after reading, 30 pages are left.
- Therefore, \( \frac{1}{8}x = 30 \).

7. **Solve for \( x \)**:
- Multiply both sides by 8 to isolate \( x \):
- \( x = 30 \times 8 = 240 \).

Thus, the total number of pages in the book is **240 pages**.

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