Institution: জগন্নাথ বিশ্ববিদ্যালয় Exam: C ইউনিট : 2017-2018
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

The equation \( 2x = 3y = 4z \) indicates that \( 2x \), \( 3y \), and \( 4z \) are equal to a common value, which we can denote as \( k \).

We can express \( x \), \( y \), and \( z \) in terms of \( k \):

1. From \( 2x = k \), we get:
\[
x = \frac{k}{2}
\]

2. From \( 3y = k \), we find:
\[
y = \frac{k}{3}
\]

3. From \( 4z = k \), we obtain:
\[
z = \frac{k}{4}
\]

Now, substituting \( x \), \( y \), and \( z \) in terms of \( k \), we have:
\[
x : y : z = \frac{k}{2} : \frac{k}{3} : \frac{k}{4}
\]

To simplify the ratio, we can eliminate \( k \) and find a common denominator. The least common multiple of 2, 3, and 4 is 12. Now we can rewrite each term with a denominator of 12:
- \( x = \frac{k}{2} = \frac{6k}{12} \)
- \( y = \frac{k}{3} = \frac{4k}{12} \)
- \( z = \frac{k}{4} = \frac{3k}{12} \)

Thus, the ratio becomes:
\[
x : y : z = 6 : 4 : 3
\]

Therefore, the ratio \( x : y : z \) is correctly given by \( 6 : 4 : 3 \), corresponding to option C.