Question : The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. What is the difference of the numbers?
Option 1: 1
Option 2: 3
Option 3: 6
Option 4: 8
Correct Answer: 6
Solution :
Given: The ratio between the two numbers is 3 : 4.
If each number is increased by 6, the ratio becomes 4 : 5.
Let the numbers be $3x$ and $4x$.
As per given conditions,
⇒ $\frac{3x+6}{4x+6}=\frac{4}{5}$
⇒ $15x+30=16x+24$
$\therefore x = 6$
$\therefore$ Required difference $=4x-3x=x=6$
Hence, the correct answer is 6.
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