Ex. 1. Rajeev's age after 15
years will be 5 times his age 5 years back.
What is the
present
age of Rajeev ? (Hotel Management,2002)
Sol. Let Rajeev's present age be x years.
Then,
Rajeev's age after 15 years = (x
+ 15) years.
Rajeev's age 5 years back = (x - 5) years.
:. x + 15 = 5 (x - 5) óx + 15 = 5x - 25 ó 4x = 40 ó x = 10.
Hence, Rajeev's present age = 10
years.
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) ó 3x -18 = x + 10 ó 2x = 28 ó 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
\ (3x + 3 + 3) = 2 (x + 3) + 10 ó 3x + 6 = 2x + 16 ó x = 10.
Hence, father's present age = (3x
+ 3) = ((3 ´ 10) + 3) years =
33 years.
Ex. 5. Rohit
was 4 times as old as his son 8 years ago. After 8 years,
Rohit will be
twice as old as his son. What
are their present ages?
Sol. Let son's age 8 years ago be x years.
Then, Rohit's age 8 years ago = 4x years.
Son's age after 8 years = (x + 8)
+ 8 = (x + 16) years.
Rohit's age after 8 years = (4x
+ 8) + 8 = (4x+ 16) years.
\ 2 (x + 16) = 4x + 16 ó 2x = 16 ó x = 8.
Hence, son's 'present age = (x +
8) = 16 years.
Rohit's present age = (4x
+ 8) = 40 years.
Ex.
6. One year ago, the ratio of Gaurav’s and Sachin’s
age was 6: 7 respectively.
Four years hence, this ratio
would become 7: 8. How old is Sa chin ?
(NABARD,
2002)
Sol:
. Let Gaurav's and
Sachin's ages one year ago be 6x and 7x years respectively. Then, Gaurav's age
4 years hence = (6x + 1) + 4 = (6x +
5) years.
Sachin's age 4 years hence = (7x
+ 1) + 4 = (7x + 5) years.
6x+5 = 7 ó 8(6x+5) = 7 (7x
+ 5) ó 48x + 40 = 49x + 35 ó x = 5.
7x+5 8
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.
\x + 16) = 3 (5x + 16) ó 7 (x + 16)
= 3 (5x + 16)
ó 7x + 112 = 15x + 48
7
ó 8x = 64 ó x = 8.
Hence, Abhay's father's
present age = (5x + 10) = 50 years.