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Problems on Ages Questions and Answers

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81.


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 ?

Answer: C

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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82.

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 ?

Answer: C

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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83.

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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84.

A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's husband age is ?

Answer: C

By trial and error method from the given options, 

as \(54-45=\left ( \frac{1}{11} \right )*\left ( 45+54 \right )=\frac{99}{11}=9\) 

Hence this satisfies the given conditions.

Then the woman's husband age is 54.

 

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85.

The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?

Answer: A

Write the condition algebraically.

\[ A + B = (B + C) + 12 \]

The \( B \) cancels from both sides:

\[ A - C = 12 \]

So C is 12 years younger than A. B's age never matters - which is why it is not given.

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86.

The ratio of Karthik’s and Kalyan’s ages is 4: 5. If the difference between the present age of Kalyan and the age of Karthik 5 years hence is 3 years, then what is the total of present ages of Karthik and Kalyan?

Answer: D

Let us consider Karthik as K1 and Kalyan as K2.

Given \(\frac{k1}{8+k1}\) and \(K2 - (K1 + 5) = 3 \)

\(K2 - K1 = 8\)

\(K2 = 8 + K1\)

Now,

\(\frac{k1}{8+k1}\) = \(\frac{4}{5}\)

k1 = 32 years

\(\therefore k2=40\) years 

k1 + k2  = 72 years

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87.

The average of the ages of Sumit, Krishna and Rishabh is 43 years and the average of the ages of Sumit, Rishabh and Rohit is 49 years. If Rohit is 54 years old, what is Krishna'a age ? 

Answer: B

Let present ages of Sumit = \(w\), Krishna = \(x \), Rishabh = \(y\) and Rohit = \(z\) , then

\(w+x+y = 43*3 = 129 ..(i)\)

\(w+y+z = 49*3 = 147 ..(ii)\)

Subtracting (i) from (ii),
\((w+y+z) - (w+x+y)=147 -129 , z- x =18 ..(iii)\)

Given Rohit's age => z = 54, so from (iii), x = 54-18 = 36

 

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88.

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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89.

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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90.

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 ?

Answer: C

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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