One-half of a certain number is equal to 65% of the second number. What is the ratio of the first number to second number?

13:10

The correct answer is Option (1) → 13:10

Let the first number = A and the second number = B.

Given:

$\frac{1}{2}A = 65\% \text{ of } B$

Convert percentage to fraction:

$65\% = \frac{65}{100} = \frac{13}{20}$

So,

$\frac{A}{2} = \frac{13}{20} B$

Multiply both sides by 20:

$10A = 13B$

Now write the ratio $A : B$:

$A : B = 13 : 10$