**Explanation:**

To understand why the correct answer is option 'D', let's first define what it means for two numbers to be coprime.

**Coprime Numbers:**
Two numbers are said to be coprime or relatively prime if their greatest common divisor (GCD) is 1. In other words, there is no number other than 1 that divides both of them.

Now, let's consider two coprime numbers, say a and b, and a number n that is divisible by both a and b. We need to determine whether n is divisible by their difference, sum, quotient, or product.

**Divisibility by Difference:**
Let's assume the difference between a and b is d. In this case, we can express a as b + d. If n is divisible by both a and b, we can write n as a multiple of a and b:

n = k1 * a
n = k2 * b

Substituting a = b + d in the first equation, we get:

n = k1 * (b + d)

Since n is a multiple of both a and b, it must also be a multiple of d (the difference between a and b). Therefore, the difference between two coprime numbers does not necessarily divide n.

**Divisibility by Sum:**
Similarly, let's assume the sum of a and b is s. In this case, we can express a as s - b. If n is divisible by both a and b, we can write n as a multiple of a and b:

n = k1 * a
n = k2 * b

Substituting a = s - b in the first equation, we get:

n = k1 * (s - b)

Since n is a multiple of both a and b, it must also be a multiple of s (the sum of a and b). Therefore, the sum of two coprime numbers does not necessarily divide n.

**Divisibility by Quotient:**
Now, let's assume the quotient of a and b is q. In this case, we can express a as q * b. If n is divisible by both a and b, we can write n as a multiple of a and b:

n = k1 * a
n = k2 * b

Substituting a = q * b in the first equation, we get:

n = k1 * (q * b)

Since n is a multiple of both a and b, it must also be a multiple of q (the quotient of a and b). Therefore, the quotient of two coprime numbers does not necessarily divide n.

**Divisibility by Product:**
Finally, let's consider the product of a and b, which is ab. If n is divisible by both a and b, we can write n as a multiple of a and b:

n = k1 * a
n = k2 * b

Multiplying these equations, we get:

n * n = (k1 * a) * (k2 * b)
n^2 = k1 * k2 * a * b

Since n^2 is a multiple of both a and b, it must also be a multiple of ab (the product of a and b). Therefore, the product of two coprime numbers divides n.

Hence, the correct answer is option 'D

D is correct option
Example: 5 and 7
70 is divisible by 5 and 7
5×7=35
70 is divisible by 35