Question

the sum of the present age of a boy and his father is 70 years. 5years later the product of their age will be 1200 years. Find their present ages​

Answer 1

Answer:

• The father is 55 years old.

• The boy is 15 years old.

Step-by-step explanation:

(Taking the age of the boy as b and his father's age as f)

Using the given information, the below equations form:

• b + f = 70

• (b + 5)(f + 5) = 1200

⇒ bf + 5b + 5f + 25 = 1200

⇒ bf + 5b + 5f = 1175

⇒ bf + 5(b + f) = 1175

⇒ bf + 5(70) = 1175       (substituting values)

⇒ bf + 350 = 1175

⇒ bf = 825

Now that we know the sum of there ages is 70 and the product of their ages is 825, we can derive their ages by the hit and trial method.

825 has exactly 12 factors: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

We need to find a pair from these factors that adds up to 70.

Clearly, that pair is 55 and 15.

Hence, the age of the father is 55 years and the age of the boy is 15 years. Hope it helps!