Two numbers are in the ratio 2 : 3. If 3 be added to both of them, then their ratio becomes 3 : 4. Find the sum of the numbers.

Given:

The ratio of two numbers = 2 : 3

When 3 is added to both, the new ratio = 3 : 4

Calculation:

Let the two numbers be 2x and 3x.

According to the question,

\(\frac{(2x + 3)}{(3x + 3)} = \frac{3}{4}\)

⇒ 4(2x + 3) = 3(3x + 3)

⇒ 8x + 12 = 9x + 9

⇒ 9x - 8x = 12 - 9

⇒ x = 3

Thus, the numbers are 2x = 2(3) = 6 and 3x = 3(3) = 9.

The sum of the numbers = 6 + 9 = 15.

The sum of the numbers is 15.