Question

If (3a-5b) : (3a+5b)=1:4 then find the value of a:b​

Answer 1

a : b = 25 : 9

Explanation:

(3a - 5b) : (3a + 5b) = 1 : 4

Product of extremes = product of means

(3a - 5b) *4 = (3a +5b) * 1 {Distributive property}

3a * 4 - 5b*4 = 3a + 5b

12a - 20b = 3a + 5b

Add 20b to both sides

12a = 3a + 5b + 20b

12a = 3a + 25b

Subtract 3a from both sides

12a - 3a = 25b

9a = 25b

`(a)/(b)=(25)/(9)`

a:b = 25 : 9