Which of the following ratios is equivalent to 3 : 2?

To find which ratio is equivalent to 3 : 2, we can simplify each given option by dividing both numbers in the ratio by their greatest common divisor (GCD), or check if multiplying both terms of 3 : 2 by the same non-zero integer yields the given ratio.

Step 1: Understand the given ratio
The given ratio is:
3 : 2
This can also be written in fractional form as:
$\frac{3}{2}$

Step 2: Test each option

Option 1: 53 : 38
53 is a prime number, so the ratio 53 : 38 cannot be simplified further.
$\frac{53}{38}\ne \frac{3}{2}$

Option 2: 51 : 37
37 is a prime number and does not divide 51, so 51 : 37 cannot be simplified.
$\frac{51}{37}\ne \frac{3}{2}$

Option 3: 52 : 34
Dividing both terms by 2 gives:
52 ÷ 2 = 26
34 ÷ 2 = 17
So, 52 : 34 simplifies to 26 : 17.
$\frac{26}{17}\ne \frac{3}{2}$

Option 4: 54 : 36
Dividing both terms by 18 (their greatest common divisor):
54 ÷ 18 = 3
36 ÷ 18 = 2
So, 54 : 36 simplifies exactly to 3 : 2.
Alternatively, multiplying both terms of 3 : 2 by 18 gives:
3 × 18 = 54
2 × 18 = 36
Thus, 54 : 36 is equivalent to 3 : 2.

Conclusion:
The correct equivalent ratio is 54 : 36.