Ten years ago A was half of B in age. If the ratio of their present ages is…

Let the present age of A be x and age of B be y.

Ten years ago A was half of B in age

x - 10 = (y - 10)/2

Cross multiplication

2 (x - 10) = (y - 10)

2x - 20 = y - 10

2x - y = 20 - 10

2x - y = 10

2x = 10 + y …Eq..1

The ratio of their present ages is 3 : 4

x / y = 3/4

Cross multiplication

4x = 3y

x = 3y/4…..Eq..2

Substitute the value of x from Eq..2 to Eq..1

2 (3y/4) = 10 + y

3y/2 = 10 + y

Cross multiplication

3y = 2 (10 + y)

3y = 20 + 2y

3y - 2y = 20

y = 20

The age of B is 20 years.

Substituting the value of y in Eq..2 to derive value of x

x = 3y/4

x = 3 × 20/4

x = 3 × 5

x = 15

The age of A is 15 years.

The age of A is 15 years and age of B is 20 years.

Hence Sum of their ages is 15+20 = 35 years