In a library `60%` of the books are in Hindi, `60%` of the remaining are in English and rest of the books are in Urdu. If 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, we will break down the information given and calculate the 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 represented as \( T \).

### 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 can be calculated as:
\[ \text{Books in Hindi} = 60\% \text{ of } T = 0.6T \]

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

### 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 can be calculated as:
\[ \text{Books in English} = 60\% \text{ of Remaining books} = 0.6 \times 0.4T = 0.24T \]

### Step 5: Set up the equation based on the number of English books.
We know from the problem statement that there are 3600 books in English. Thus, we can set up the equation:
\[ 0.24T = 3600 \]

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

### Step 7: Calculate the number of books in Urdu.
Now that we have the total number of books, we can calculate the number of books in Urdu. We already know that:
\[ \text{Remaining books after Hindi} = 0.4T \]
And we have calculated the number of books in English as \( 0.24T \). Therefore, the number of books in Urdu is:
\[ \text{Books in Urdu} = \text{Remaining books} - \text{Books in English} = 0.4T - 0.24T = 0.16T \]

### Step 8: Substitute \( T \) to find the number of books in Urdu.
Substituting \( T = 15000 \):
\[ \text{Books in Urdu} = 0.16 \times 15000 = 2400 \]

### Final Answer:
The total number of books in Urdu is \( 2400 \).

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