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?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 13:10
Write the statement as an equation in the two numbers; dividing both sides by the second number then gives the ratio directly.
Let the numbers be \(x\) and \(y\): \(\displaystyle \frac{1}{2}x=\frac{65}{100}y\)
\(\displaystyle \frac{x}{y}=\frac{65}{100}\times2=\frac{130}{100}=\frac{13}{10}\), that is, \(x:y=13:10\)
Tip: Half the first number equals 65% of the second, so the first number must be the larger one; that alone rules out 8:13 and 10:13.