__Chapter-8__

__Problem Based On Ages__

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__Introduction- __

**Some questions are given in competitive exams which are based on ages so; here we represented some examples which will be helpful to solve these type of questions.**

__Example:____ __The ratio of present age of A & B is 2: 3 the present age of A is 30 years. Find the age of B after 5 years?

__Answer:__

__Step 1:__** ** A: B present age ratio is 2: 3 and A = 30 years.

**B present age is 30 / 2 x 3 = 45 years.**

__Step 2:__**B age after 5 years is 45 + 5 = 50 years.**

__Step 3:__

** Example:** Vineet is as younger to Garima as she is older to Devyani .If the sum of the ages of Garima&Devyani is 58 years. What is Vineet age?

__Answer:____Step 1:____ __G – V = V – D

** Step 2:** G + D = 2V

__Step 3:__**58 = 2V**

**V = 29 years**

__Step 4:____Example:__

Ayush and Vivek is 50 years old and 70 years old . How many years before was the ratio of their ages 3: 5?

__Answer:__

Their ratio was 3 : 5 , t years before ,

So, 50 – t / 70 – t = 3 / 5

5 ( 50 – t ) = 3 ( 70 – t )

250 – 5t = 210 – 3t

2t = 40

t = 20 years.

__Example:__

Robin is 28 years old and Reshma is 12 years . In how many years will Robin be twice as old as Reshma?

__Answer:__

Let Robin be in x years .

Then, (28 + x) = 2 (12 + x)

28 + x = 24 + 2x

x = 4 years .

__Example:__

Ratio of ages of Meena& Neeta 4 years ago was 3 : 5. If the sum of present ages of Meena& Neeta is 64 years than, Find the present ages of Meena& Neeta.

__Answer:__

Let the ages is Meena& Neeta 4 years ago are 3x and 5x.

Hence,( 3x + 4 )+( 5x + 4 ) = 64 years,

= 8x + 8 = 64, = 8x = 56, x = 7. (We get the value of x).

So the age of Meena, 4 years ago = 7 x 3 = 21years,

and the age of Neeta, 4 years ago = 7 x 5 = 35 years.

Now the present age of Meena is = (21 + 4) = 25 years,

and present age of Neeta is = ( 35 + 4) = 39 years.

__Example:__

At present , the ratio between the ages of Anil and Anu is 4 : 3 . After 4 years , Anil’s age will be 24 years . What is the age of Anu at present?

__Answer:__

Let the present age of Anil and Anu is 4x years and 3x years respectively.

So , After 4 years Anil’s age ,will be 24 ,

4x + 4 = 24

4x = 20

x = 5

So , Anu present age is 3x = 3 x 5 = 15 years .

__Example:__

Seven years ago , the age ratio of Sonali and Monali was 6 : 5 . Three years hence, the ratio of their ages will be 11: 10 . What is Monali‘s age at present?

__Answer:__

Let the age of Sonali and Monali 7 years ago be 6x and 5x years respectively .

So, (6x + 7) + 3 /(5x + 7 ) + 3 = 11 / 10

10 ( 6x + 10) = 11 ( 5x + 10 )

5x = 10

x = 2

So, Monali‘s present age = ( 5x + 7 ) = 17 years .

__Example:__

12 years hence , Bharat will be just five times as old as he was 12 years ago , His present age is ?

__Answer:__

Let Bharat present age be x years .

Bharat age 12 years ago = ( 12 – x ) years and his age 15 years hence = ( 12 + x ) .

So, (12 + x) = 5 (12 – x)

12 + x = 60 – 5x

6x = 48

x = 8

So , Bharat present age is 8 years .

__Example:__

Ratio of present ages of C & D is 4 : 6 . The present age of C is 40 years. Find the age of D after 6 years.

__Answer:__

Let the ages of C & D are 4x and 6x.

Hence, C = 4x = 40, = x = 10, (So we get the value of x)

So the present age of D is = 6x = 6 X10 = 60 years, hence the age of D is after 6 years 60 + 6 = 66 years.

__Example:__

The ratio between the present ages of A and B is 6 : 7 . If B is 4 years old than A, What will be the ratio of the ages of A and B after 4 years?

__Answer:__

** Step 1:**Let the A’s age and B’s age be 6x and 7x years respectively . Then, 7x – 6x = 4 . S0, x = 4

**Required ratio = ( 6x + 4 ) : ( 7x + 4 ) = 28 : 32 = 7 : 8 .**

__Step 2 :____Example:__

The ratio of mother age to his son’s age is 7 : 3 . The product of their ages is 756 . The ratio of their ages after 6 years will be?

__Answer:__

__Step 1 :____ __Let the present ages of the mother and son be 7x and 3x years respectively .

Then, 7x X 3x = 756

21×2 = 756

= x^{2} = 36

= x = 6

** Step 2 :** Required ratio = (7x + 6 ) : ( 3x + 6 ) = 48 : 24 = 2 : 1 .