In a library 60% of the books are in Hindi, 60% of the remaining are in English and rest of the books are in there are 3600 books in English, then the total no. of books in Urdu are :

Options

A. 2400
B. 2500
C. 3000
D. none of these

Answer

To solve the problem step by step, let's break down the information given and find the total number of books in Urdu.

### Step 1: Determine the total number of books in the library.
Let the total number of books in the library be \( X \).

### Step 2: Calculate the number of books in Hindi.
According to the problem, 60% of the books are in Hindi. Therefore, the number of books in Hindi is:
\[ \text{Books in Hindi} = 0.6X \]

### Step 3: Calculate the remaining books after Hindi.
The remaining books after accounting for Hindi books are:
\[ \text{Remaining books} = X - 0.6X = 0.4X \]

### Step 4: Calculate the number of books in English.
It is given that 60% of the remaining books are in English. Therefore, the number of books in English is:
\[ \text{Books in English} = 0.6 \times 0.4X = 0.24X \]

### Step 5: Set up the equation based on the number of English books.
We know that the number of books in English is given as 3600. So, we can set up the equation:
\[ 0.24X = 3600 \]

### Step 6: Solve for \( X \).
To find \( X \), divide both sides of the equation by 0.24:
\[ X = \frac{3600}{0.24} = 15000 \]

### Step 7: Calculate the number of books in Urdu.
Now that we have the total number of books \( X \), we can find the number of books in Urdu. First, we need to find the total number of books in Hindi and English:
- Books in Hindi: \( 0.6X = 0.6 \times 15000 = 9000 \)
- Books in English: \( 0.24X = 3600 \)

Now, we can find the number of books in Urdu:
\[ \text{Books in Urdu} = X - (\text{Books in Hindi} + \text{Books in English}) = 15000 - (9000 + 3600) = 15000 - 12600 = 2400 \]

### Final Answer:
The total number of books in Urdu is **2400**.

---