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» (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»

(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.