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# Problems on Ages

1.

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

Let C's age be $$x$$ years. Then, B's age = $$2x$$ years. A's age $$=(2x+2)$$ years.

$$\therefore (2x + 2) + 2x + x = 27$$

$$\Rightarrow 5x = 25$$

$$\Rightarrow x=5$$

Hence, B's age $$=2x=10$$ years.

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2.

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 ?

Let varun's age = $$x$$ years.

From the given conditions,

$$\Rightarrow x+1 = 2(x-12)$$

$$\Rightarrow x=25$$ years.

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3.

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 ?

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

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4.

Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?

Ayush's present age = 10 years.

His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.

Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.

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5.

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is

Let the son's present age be $$x$$ years .
Then, man's present age = $$(x + 24)$$ years

$$\Rightarrow (x + 24) + 2 = 2(x + 2)$$

$$\Rightarrow x + 26 = 2x + 4$$

So, $$x = 22$$

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6.

Sivagami is 2 years elder than Meena. After 6 years the total of their ages will be 7 times . Then age of Sivagami is :

Let Meena’s age = $$A$$

Then Sivagami’s age =  $$A+2$$

After 6 years the total of their ages will be 7 times of what?
Not clear.

So the given data are inadequate.

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7. Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

Let John's present age be  $$x$$

$$\therefore$$ $$x-5=$$ $$\frac{1}{2}\left ( x+8 \right )$$

$$\Rightarrow$$ $$x-5=$$ $$\frac{1}{2}x +4$$

$$\Rightarrow$$ $$\frac{1}{2}x=9$$

$$\Rightarrow$$ $$x=18$$

Hence, John's is 18 years old.

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8.

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question : R - Q = ? .

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined.

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9.

If 6 years are subtracted from the present age of Arun and the remainder is divided by 18, then the present age of his grandson Gokul is obtained. If Gokul is 2 years younger to Madan whose age is 5 years, then what is the age of Arun ?

Let the Present age of arun is  $$x$$

Gokul's age = 5-2 = 3
$$\therefore$$  $$\frac{x-6}{18}=3$$

$$\Rightarrow x-6=54$$

$$x=60$$

Arun's present age = 60 years

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10.

Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present age?

Let present age of P and Q be $$3x$$ and $$4x$$ respectively.

$$\left ( 3x-10 \right )=\frac{1}{2}\left ( 4x-10 \right )$$

$$\Rightarrow$$ $$6x-20=4x-10$$

$$\Rightarrow$$ $$2x=10$$

$$\Rightarrow$$ $$x=5$$

Total of their present age is
$$=3x+4x=7x=7×5=35$$

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