Two number are in the ratio of 2 : 3. If 9 is added to each number, they will be in the ratio 3 : 4. What is the product of the two numbers?

Let the number be M and N
According to the question.
M/N = 2/3
⇒ 3M = 2N
⇒ 3M - 2N = 0 ...(i)
And (M + 9)/(N + 9) = 3/4
⇒ 4M + 36 = 3N + 27
⇒ 4M - 3N = -9 ...(ii)
Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27
Now, putting N = 27 in Eq. (i), we get 3M = 54
⇒ M = 18
∴ Product of the given numbers = 27 x 18 = 486