If (a - b) : (a + b) = 1 : 11, find the ratio (5a + 4b + 15) : (5a - 4b +3) .

The given problem is based on the ratio of two numbers.

Answer: If (a - b) : (a + b) = 1 : 11, then the ratio (5a + 4b +15) : (5a - 4b + 3) = 5 : 1

Let us find (5a + 4b + 15) : (5a - 4b + 3).

Explanation:

The ratio formula for any two quantities say a and b is given as,  a : b = a / b

Given that, (a - b) : (a + b) = 1 : 11

(a - b) / (a + b) = 1 /11

11(a - b) = 1(a + b)       --------> By cross multiplication

11a - 11b = a + b

11a - a = 11b + b

10a = 12b                 --------> Divide by 2 on both sides.

5a = 6b

Now let us move on to (5a + 4b + 15) : (5a - 4b + 3)

(5a + 4b +15) / (5a - 4b +3)

(6b + 4b +15) / (6b - 4b +3)

(10b + 15) / (2b + 3)

5(2b + 3) / (2b + 3)       --------> Taking 5 common in the nuemerator.

5/1

= 5 : 1

So, (5a + 4b + 15) : (5a - 4b + 3) = 5 : 1

Thus, ratio (5a + 4b + 15) : (5a - 4b + 3) is equivalent to 5 : 1 .