The ratio of two numbers is 4 : 5. If 6 is added to both the numbers, then their ratio becomes 6 : 7. Find the smallest original number (before addition).

Correct option is B

Given:
Original ratio of two numbers = 4 : 5
After adding 6 to both numbers, the new ratio = 6 : 7
​Solution:
Let the original numbers be 4x and 5x .
When 6 is added to both, the numbers become 4x + 6 and 5x + 6, and their ratio is 6:7.
$$\frac{4x + 6}{5x + 6} = \frac{6}{7}$$​
7(4x + 6) = 6(5x + 6)
28x + 42 = 30x + 36
28x - 30x = 36 - 42
-2x = -6
x = 3
First number = 4x $$= 4 \times 3 = 12$$​​
Second number = 5x $$= 5 \times 3 = 15$$​​
The smallest original number is 12.