A sample of DNA has the ratio of `(AT)/(GC)` is 0.8 . If the no. of moles of adenine in a sample is 25000. What is the no. of moles of cytosine in it

Options

A. 50000
B. 40000
C. 31250
D. 62500

Answer

To solve the problem step by step, we will use the information given about the ratio of adenine to guanine (A to G) and cytosine to thymine (C to T) in the DNA sample.

### Step 1: Understand the Ratio
The ratio of (A + T) to (G + C) is given as 0.8. This means:
\[ \frac{A + T}{G + C} = 0.8 \]

### Step 2: Express the Relationship
Since adenine (A) pairs with thymine (T) and guanine (G) pairs with cytosine (C), we can express:
- A = T (since they pair)
- G = C (since they pair)

Let’s denote:
- A = number of moles of adenine
- T = number of moles of thymine
- G = number of moles of guanine
- C = number of moles of cytosine

From the pairing, we can say:
\[ A + T = 2A \quad \text{and} \quad G + C = 2C \]

### Step 3: Substitute into the Ratio
Now substituting into the ratio:
\[ \frac{2A}{2C} = 0.8 \]
This simplifies to:
\[ \frac{A}{C} = 0.8 \]

### Step 4: Find the Number of Moles of Cytosine
We know the number of moles of adenine (A) is given as 25,000. We can express C in terms of A:
\[ C = \frac{A}{0.8} \]

Substituting the value of A:
\[ C = \frac{25000}{0.8} \]

### Step 5: Calculate C
Calculating the above expression:
\[ C = 25000 \div 0.8 = 31250 \]

Thus, the number of moles of cytosine (C) is **31,250**.

### Final Answer
The number of moles of cytosine in the sample is **31,250**.

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