Question

The difference between the ages of a man and his son is 30 years. In 5 years time the ratio of their ages will be 3 :1.
(A)
how old are they now
B) find the sum of their ages ​

Answer 1

Let the age of the man be x and the age of the boy be y,

Then according to the question, their difference is 30 so,

$x - y = 30 \: \: (eq.1)$

Now, after five years = x+5 and y+5, Their ratio is 3 : 1, So,

$\frac{x + 5}{y + 5} = \frac{3}{1} \\ \\ x + 5 = 3y + 15 \: \: (cross \: multiply) \\ \\ x - 3y = 10 \: (eq.2) \\ \\ now \: eq.2 - eq.1 \\ \\ \: \: \: \: x - 3y = 10 \\ - x + y \: = - 30 \\ \\ - 2y = - 20 \\ \\ y = 10$

Now we have y = 10

Put y = 10 in x - y = 30 (eq.1)

So, x - 10 = 30

x = 30 + 10

x = 40

So, The present age of the Man is 40 years and his son is 10 years.

The sum of their ages is = 40 + 10 = 50 years.

!!!!!!!! Mark as brainliest !!!!!!!!