Out of the total books, 20% of books are of type-1. 30% of remaining books are of type-2. 60% of remaining books are of type-3. The remaining 448 books are of type-4. How many total books are there?

Options

A. 1000
B. 2000
C. 1500
D. 1800

Answer

To find the total number of books, let's denote the total number of books as \( X \).

1. **Calculate Type-1 Books**:
- 20% of the total books are of Type-1.
- Therefore, the number of Type-1 books is:
\[ \text{Type-1 books} = 0.2X \]

2. **Calculate Remaining Books After Type-1**:
- The remaining books after accounting for Type-1 books is:
\[ \text{Remaining books} = X - 0.2X = 0.8X \]

3. **Calculate Type-2 Books**:
- 30% of the remaining books are of Type-2.
- Therefore, the number of Type-2 books is:
\[ \text{Type-2 books} = 0.3 \times 0.8X = 0.24X \]

4. **Calculate Remaining Books After Type-2**:
- The remaining books after accounting for Type-2 books is:
\[ \text{Remaining books} = 0.8X - 0.24X = 0.56X \]

5. **Calculate Type-3 Books**:
- 60% of the remaining books are of Type-3.
- Therefore, the number of Type-3 books is:
\[ \text{Type-3 books} = 0.6 \times 0.56X = 0.336X \]

6. **Calculate Remaining Books After Type-3**:
- The remaining books after accounting for Type-3 books is:
\[ \text{Remaining books} = 0.56X - 0.336X = 0.224X \]

7. **Set Remaining Books Equal to Type-4 Books**:
- We know that the remaining books are 448, which are of Type-4.
- Therefore, we can set up the equation:
\[ 0.224X = 448 \]

8. **Solve for \( X \)**:
- To find \( X \), divide both sides by 0.224:
\[ X = \frac{448}{0.224} = 2000 \]

Thus, the total number of books is \( \boxed{2000} \).