A and B are two college friends met after 4 years of their college. C is the wife of A. Sum of ages of A, B and C at the end of college is 74 years. At the same time ratio of ages of B and C is 7:5. If present age of A is 30 years find the ratio of age of A at the end of college and the present age of C.

Option 2 : 13 : 12

**Solution :**

**Given data :**

A + B + C = 74 years ----(4 years ago)

B:C = 7:5 ----(4 years ago)

The present age of A = 30 years

**Calculation :**

The present age of A = 30 years

⇒ Age of A at the end of college (4 years ago) = 30 – 4

⇒ 26 years (1)

A + B + C = 74 years ----(4 years ago)

B + C = 74 – 26

⇒ 48 years

B:C = 7:5 ----(4 years ago)

⇒ B = 7x and C = 5x

⇒ B + C = 7x + 5x

⇒ 12x = 48 years

⇒ x = 4 years

⇒ B = 7 × 4 = 28 years (4 years ago)

⇒ C = 5 × 4 = 20 years (4 years ago)

⇒ Present age of C = 20 + 4

⇒ 24 years (2)

(age of A at the end of college):(the present age of C)

⇒ 26:24

⇒ 13 : 12

**∴ The ratio of age of A at the end of college to the present age of C is 13:12.**