Question

Two numbers are in the ratio 3 : 5. If 5 is added to each of the numbers, then the ratio becomes 2 : 3. Find the numbers.

Answer 1

Here, let the two numbers be:

3x and 5x (since they are in the ratio 3 : 5)

According to the given condition:

`(3x + 5)/(5x + 5) = 2/3`

Thus, cross-multiplying the above expression,

3(3x + 5) = 2(5x + 5)

9x + 15 = 10x + 10

9x − 10x = 10 − 15

−x = −5

∴ x = 5

Substituting, x = 5 in 3x and 5x, we get:

3x = 3(5) = 15

5x = 5(5) = 25

Hence, the numbers are 15 and 25.