Question

Two numbers are in the ratio 3:5.if 8 is added to each number , the ratio becomes 2:3. find the 2 numbers.

Answer 1

$Let \: the \: numbers \: be \: 3x \: and \: 2x. \\ Now, \: according \: to \: the \: question, \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{3x + 8}{5x + 8} = \frac{2}{3} \\ = > 3(3x + 8) =2 (5x + 8) \\ = > \: \: \: 9x + 24 = 10x + 16 \\ = > 10x - 9x = 24 - 16 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 8 \\ \\ So, \: the \: two \: numbers \: are \: \\ 3x = 3 \times 8 = 24 \: \: \: \: and \\ 5x = 5 \times 8 = 40$

$\huge{\purple{\boxed{Answer: \: 24 \: and \: 40}}}$

Answer 2

Answer:

Step-by-step explanation:

Let the two numbers be 'a' and 'b'

a : b = 3:5 then a/b = 3/5

5a = 3b then a = 3b/5

By adding 8 the ratio becomes 2:3

(a + 8) : (b +8) = 2:3

(a+8)3 = (b+8)2

3a + 24 = 2b + 16

3a - 2b +24 - 16 = 0

3a - 2b +8 = 0

3x3b/5 -2b + 8 = 0

9b -10b +40 = 0

b = 40 then b = 40 is in a = 3b/5

a = 3x40/5

a = 120/5 then a = 24

Hence a = 24 & b = 40