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**PROBLEMS ON AGES**

**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**(A.A.O. Exam,2003)

*times as old as the younger*one,*find their present ages.* 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**(S.B.I.P.O,1999)

*years, what is Nikita’s age?*Sol. Let Ankit’s age be x years. Then, Nikita’s age = 240/xyears.

2 ´ (240 /x ) – x = 4 ó 480 – x

^{2}= 4x ó x^{2}+ 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. R**

*ohit 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.