The sum of the ages of a father and his son is 100 yr now. 5 yr ago, their ages were in the ratio of 2: 1. Find the ratio of the ages of father and son after 10 yr. একজন বাবা ও তার ছেলের বর্তমান বয়সের যোগফল 100 বছর। 5 বছর আগে তাদের বয়সের অনুপাত ছিল 2 : 1। তবে 10 বছর পরে বাবা ও ছেলের বয়সের অনুপাত কত হবে?

Let present age of father = F yr
Let present age of son = S yr

Given:
\( F + S = 100 \)

5 yr ago ratio was 2 : 1
\( \frac{F - 5}{S - 5} = \frac{2}{1} \)

So,
\( F - 5 = 2(S - 5) \)
\( F - 5 = 2S - 10 \)
\( F = 2S - 5 \)

Substitute in first equation:
\( 2S - 5 + S = 100 \)
\( 3S = 105 \)
\( S = 35 \)

Then,
\( F = 100 - 35 = 65 \)

After 10 yr:
Father = \(65 + 10 = 75\)
Son = \(35 + 10 = 45\)

Required ratio:
\( 75 : 45 = 5 : 3 \)

Correct Answer: Option B (5 : 3)