5 years hence, the age of a man shall be 3 times the age of his son wh

1.	5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is (a) 45 years (b) 50 years (c) 47 years (d) 40 years
Answer» Correct answer = (d) 40 years Let the man’s present age be x years. Let his son’s present age be y years. Five years later: (x + 5) = 3(y + 5) ⇒ x + 5 = 3y + 15 ⇒ x – 3y = 10 ………..(i) Five years ago: (x – 5) = 7(y – 5) ⇒ x – 5 = 7y – 35 ⇒ x – 7y = –30 ………..(ii) On subtracting (i) from (ii), we get: -4y = -40 ⇒ y = 10 On substituting y = 10 in (i), we get: x – 3 × 10 = 10 ⇒ x – 30 = 10 ⇒ x = (10 + 30) = 40 years Hence, the man’s present age is 40 years

5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is (a) 45 years (b) 50 years (c) 47 years (d) 40 years

Answer»

Correct answer = (d) 40 years

Let the man’s present age be x years.

Let his son’s present age be y years.

Five years later:

(x + 5) = 3(y + 5)

⇒ x + 5 = 3y + 15

⇒ x – 3y = 10 ………..(i)

Five years ago:

(x – 5) = 7(y – 5)

⇒ x – 5 = 7y – 35

⇒ x – 7y = –30 ………..(ii)

On subtracting (i) from (ii), we get:

-4y = -40 ⇒ y = 10

On substituting y = 10 in (i), we get:

x – 3 × 10 = 10 ⇒ x – 30 = 10

⇒ x = (10 + 30) = 40 years

Hence, the man’s present age is 40 years