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.
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
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(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.
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