Question

4 years ago, the ratio of A's and B's age is 5:3. The sum of the present ages of A, B and
C is 80 years. If C's present age is equal to the sum of present ages of A and B. What is
present age of A?​

Answer 1

Answer:

The present age of A is 24 years.

Step-by-step explanation:

Let the present ages of A, B and C are x, y and z respectively.

By the given conditions,

(x - 4) : (y - 4) = 5 : 3 ..... (1)

x + y + z = 80 ..... (2)

z = x + y ..... (3)

From (1), we get

(x - 4) / (y - 4) = 5/3

or, 3 (x - 4) = 5 (y - 4)

or, 3x - 12 = 5y - 20

or, 3x - 5y = - 8 ..... (4)

Using (3), from (2), we get

x + y + x + y = 80

or, x + y = 40

or, y = 40 - x

Substituting y = 40 - x in (4), we get

3x - 5 (40 - x) = - 8

or, 3x - 200 + 5x = - 8

or, 8x = 192

or, x = 24

Therefore the present age of A is 24 years.