Question

The difference between the ages of a man and his son is 30years . In 5years time,the ratio of their ages will be 3:1 (1) how old how they now (2) find the sum of their ages​

Answer 1

Answer:

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)x−y=30(eq.1)

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

\begin{gathered} \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\end{gathered}

y+5

x+5

=

1

3

x+5=3y+15(crossmultiply)

x−3y=10(eq.2)

noweq.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.

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Answer 2

Answer:

The difference between the ages of a man and his son is 30years . In 5years time,the ratio of their ages will be 3:1