Question : The difference between the two numbers is 24 while the sum of those two numbers is 120. Which of the options below can be the ratio of those two numbers?
Option 1: 3 : 5
Option 2: 3 : 2
Option 3: 4 : 5
Option 4: 5 : 8
Correct Answer: 3 : 2
Solution :
Let the numbers be $a$ and $b$.
Given: $a-b=24$............(equation 1)
$a+b=120$............(equation 2)
Adding equation 1 and 2, we get:
$2a=144$
⇒ $a=72$
Putting the value of $a$ in equation 2, we get:
$72+b=120$
⇒ $b=48$
$\therefore a:b=72:48$
$=3:2$
Hence, the correct answer is 3 : 2.
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