If the ratio of two numbers a and b is 5 : 3, then find the value of (3a − 2b) : (6a + 2b).
Given:
Ratio of two numbers a : b = 5 : 3
Required: Value of (3a - 2b) : (6a + 2b)
Solution:
Let a = 5x, b = 3x
Then,
3a - 2b = 3(5x) - 2(3x) = 15x - 6x = 9x
6a + 2b = 6(5x) + 2(3x) = 30x + 6x = 36x
So, the required ratio:
9x : 36x = 9 : 36 = 1 : 4
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