The ratio between two number is 3 : 4. if each number is increased by 3, the ratio becomes 4 : 5. Find the differences between the numbers.

Let the number be 3k and 4k.
According to the question,
(3k + 3)/(4k+ 3) = 4/5
⇒ 5(3k + 3 ) = 4(4k + 3)
⇒ 15k + 15 = 16k + 12
∴ k = 15 - 12 = 3
∴ Difference between the numbers = (4k - 3k) = k = 3