Question

The ages of a and b are in the ratio 3: 4. if the ratio of their ages 15 years back was 3: 5, find the sum of their present ages.

Answer 1

Let the common ratio be x.
Therefore, the age of a will be 3x and that of b will be 4x.
Age of a 15 years back is 3x - 15 and that of b is 4x - 15.
Ratio of their ages 15 years back is 3: 5.
That is ,
3x-15/4x-15 = 3/5
By cross multiplication,
⇒ 5 X 3x-15 = 3 X 4x-15
⇒ 15x - 12x = -45 + 75
⇒ 3x = 30
⇒ x = 10

Hence,  the age of a = 3x = 3 X 10 = 30 and 
the age of b = 4x = 4 X 10 = 40.

Answer 2

Answer:

Let the common ratio be x.

Therefore, the age of a will be 3x and that of b will be 4x.

Age of a 15 years back is 3x - 15 and that of b is 4x - 15.

Ratio of their ages 15 years back is 3: 5.

That is ,

3x-15/4x-15 = 3/5

By cross multiplication,

⇒ 5 X 3x-15 = 3 X 4x-15

⇒ 15x - 12x = -45 + 75

⇒ 3x = 30

⇒ x = 10

Hence,  the age of a = 3x = 3 X 10 = 30 and  

the age of b = 4x = 4 X 10 = 40