Ex. 2. The ages of two persons differ by 16 years. If 6 years ago, the elder one be
3 times as old as the younger one, find their present ages.(A.A.O. Exam,2003)
Sol. Let the age of the younger person be x years.
Then, age of the elder person = (x + 16) years.
:.3 (x - 6) = (x + 16 - 6)ó3x -18 = x + 10ó2x = 28ó x = 14.
Hence, their present ages are 14 years and 30 years.
Ex. 3. The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita
is more than Ankit's age by 4 years, what is Nikita's age?(S.B.I.P.O,1999)
Sol. Let Ankit's age be x years. Then, Nikita's age = 240/xyears.
\ 2 ´ (240 /x ) – x = 4 ó 480 – x2 = 4x ó x2 + 4x – 480 = 0
ó ( x+24)(x-20) = 0 ó x = 20.
Hence, Nikita's age = (22_0) years = 12 years.1
Ex. 4. The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father..(S.S.C, 2003)
Sol. Let the son's present age be x years. Then, father's present age = (3x + 3) years
Hence, Sachin's present age = (7x + 1) = 36 years.
,7. Abhay’s age after six years will be three-seventh of his fathers age. Ten years ago the ratio of their ages was 1 : 5. What is Abhay’s father's age at present?
Sol. Let the ages of Abhay and his father 10 years ago be x and 5x years respectively. Then,
Abhay's age after 6 years = (x + 10) + 6 = (x + 16) years.
Father's age after 6 years = (5x + 10) + 6 = (5x + 16) years.