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Problems on Ages Questions and Answers

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71.

The average age of a couple is 24 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child ?

Answer: A

Five years ago the couple's ages summed to

\[ 2 \times 24 = 48 \]

Each has aged five years since, so their present total is

\[ 48 + 10 = 58 \]

The three of them now total

\[ 3 \times 20 = 60 \]

\[ \text{child} = 60 - 58 = 2 \text{ years} \]

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72.


The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years] 

Answer: D


Let, Maala’s age = \(4A\)  and  Kala's age = \(3A\)

Then, \(4A + 3A =28\)

\(A=4\)

Maala’s age = 16 years
and Kala’s age = 12 years

Proportion of their ages after 8 is = \((16 + 8) : (12 + 8)\)

\(=24:20\)

\(=6:5\)

 

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73.


The sum of the present ages of a mother and his daughter is 60 years. five years ago, mother's age was four times the age of the daughter. so now the daughter's age will be?

Answer: C

 
Let the present ages of daughter and mother be \(x\)  and  \((60-x)\) respectively .

Then,    \((60 - x) - 5= 4(x - 5)\)

\(\Rightarrow\)  \(55 - x = 4x - 20 \) 

\(\Rightarrow \)  \(5x=75\)

\(\Rightarrow x=15\)

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74.

If Riya's age is four times the age of Siya and if Riya's age is 24 yrs , find the age difference between Riya and Siya ? 
 

Answer: D

Let Siya's age = \(x\)

Then Riya's age =  \(4x\)

But given Riya's age = 24

\(\Rightarrow 4x=24\) 

\(\Rightarrow x=6\)

Hence Siya's age = 6 yrs

\(\Rightarrow\)  The age difference = 24 - 6 = 18 yrs.

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75.

The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

Answer: A

Let the present age of A and B be 5 \(x\) and 6 \(x\) respectively.

Therefore, According to problem,

5  \(x\) +  6 \(x\) = 44

\(\Rightarrow \) \(11x=44\)

\(\Rightarrow \) \(x =4\)

Present ages of A and B are 20 and 24 respectively.

After 8 years,

Ages of A and B  are (20+8) and (24+8)

A = 28 years and B=32 years

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76.

When Ram was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Ram's brother is 6 years older than Ram and his mother is 3 years younger than his father, how old was Ram's sister when Ram was born ?
 

Answer: C

Ram age when he was born = 0 years
His brother's age = 6 year

His father's age = brother age + 32years = 6+32 = 38

His mother's age = father's age - 3 = 35
So sister's age = 35-25 = 10years.

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77.

 If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,

Answer: C

Let daughter’s age = \(A\) and mother’s age = \(B\) years

Given:  \(2A+B = 70\)  and  \(A+2B = 95\)

Solving B , we will get \(B=40\)

 

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78.


The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age? [0.5 Decades = 5 Years]

Answer: C


Let, Total of current ages of the 2 daughters is  \(A\)   years.
Then, father’s current age =  3A years.

\((3A + 5) = 2 (A +10)\)

\(\Rightarrow\) \(3A + 5 = 2A + 20\)

\(\Rightarrow A = 15\)


Therefore, father’s current age = 45 years.

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79.


"I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years ?
 

Answer: B

Let the present age of the man be '\(P\)' and son be '\(Q\)',

Given, \( P + Q = 64 \) or \(Q = (64 - P)\)

Now the man says "I am five times as old as you were, when I was as old as you are",
So, \(P = 5[B - (P - Q)]\)

We get \(6P=10Q\)

Substitute value for \(Q\)

\(6P = 10(64 - P),\)
Therefore, \(P\) = 40 and \(Q\) = 24

 

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80.

Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age ?
 

Answer: B

Let Kumar’s present age be "\(x\)" years and Sailesh’s present age be "\(y\)" years.
Then, according to the first condition,

\(x - 10 = 3(y - 10) => x - 3y = - 20 ........(1)\)

Now, Kumar’s age after 10 years = \((x + 10)\) years.

Sailesh’s age after 10 years = \((y + 10)\) years.

\((x + 10) = 2 (y + 10) => x - 2y = 10 ......(2)\)

Solving (1) and (2),

we get \(x\) = 70 and \(y\) = 30

Kumar’s present age = 70 years    and  Sailesh’s present age = 30 years.
 

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