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# Problems on Ages

1.

The average age of 80 boys in a class is 15. The average age of group of 15 boys in the class is 16 and the average of another 25 boys in the class is 14. What is the average age of the remaining boys in the class ?

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File: /var/www/html/application/controllers/Questions.php
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Let the age of A = $$A$$, B = $$B$$ and C = $$C$$

From given,

$$A = 3B$$

4 years ago,

$$A + 4 = 31$$

$$\Rightarrow A=27$$

sub in above $$B$$ , we get $$B$$  = 9

$$C = 2(27 - 4) + 4 = 46 + 4 = 50$$

Hence B = 9years and C = 50years.

#### Enter details here

3.

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?

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File: /var/www/html/application/controllers/Questions.php
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File: /var/www/html/index.php
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Function: require_once

Let the age of the youngest child is '$$x$$' years.
Then the child elder than the yongest is '$$x + 3$$' yrs
Since each have 3yrs difference upto 5 children
And given that,

$$\Rightarrow x +x +3 + x+6 +x+9 + x+12 = 50$$

$$\Rightarrow 5x+30=50$$

$$\Rightarrow x= 4$$ years.

#### Enter details here

5.

Rajan's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Rajan's daughter and Rajan's mother ?

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File: /var/www/html/application/controllers/Questions.php
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Function: view

File: /var/www/html/index.php
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Function: require_once

Let Rajan's present age be '$$x$$' years.

Then his daughter's present age is =  $$\frac{x}{3}$$ years.

His mother's present age = $$\frac{13x}{9}$$ years.

Now, according to the question,
$$\therefore x+\frac{x}{3}+\frac{13x}{9}=125$$

$$\Rightarrow x=$$$$\frac{125*9}{25}$$$$=45$$

Therefore, required difference = $$\frac{13x}{9}-$$$$\frac{x}{3}=13x -$$$$\frac{3x}{9}=$$$$\frac{10x}{9}$$

$$\Rightarrow \frac{10*45}{9}$$= 50 years