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Problems on Ages Questions and Answers

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11.

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?

Answer: D

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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12.


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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13.

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?

Answer: C

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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14.

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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15.


When I was married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me.The average age of my family during my marriage is same as today. What is the age of Father when he died ?
 

Answer: B

Let the Father be \(x\) years when he died. 

Average Age 10 years ago be  \(A\)

Total Age 10 years ago = \(6A\)

Total Age after 10 years(Just before father's Death) =  \( 6A + 6*10 = 6A + 60\)

Father Died and Baby was born => the Total number of people in the family is Same (6) 
Baby born today so age of baby = 0
\((6A +60 - x)/6 = 6A/6\)

\(\Rightarrow A + 10 -(x/6) = A \)

\(\Rightarrow x/6 = 10 \)

\(\Rightarrow x = 60\)

Therefore we can conclude that the father was 60 years old when he died.

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16.

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Answer: B

Let their present ages be  \(4x, 7x \) and \(9x\) years respectively

Then, \((4x - 8) + (7x - 8) + (9x - 8) = 56\)

\(\Rightarrow 20x = 80\)

\(\Rightarrow x=4\)

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17.

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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18.

The sum of the ages of a father and son is \(45\) years. Five years ago, the product of their ages was four times the father's age at that time. The present age of father and son

Answer: C

Let son's age \(=x\) years.

Then father's age\(=(45-x)\) years.

\(\Rightarrow\) \((x-5)(45-x-5) = 4(45- x - 5)\)

\(\Rightarrow\) \((x-5)=4\)

\(\Rightarrow\) \(x=9\)

Their ages are \(36\) years and \(9\) years.

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19.

Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

Answer: A

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

then,\(\frac{ (6x + 6) + 4 }{(5x + 6) + 4}= \frac{11}{10}\)

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

\(\Rightarrow 5x = 10\)

\(\Rightarrow x = 2\)

\(\therefore\)  Sagar's present age \(= (5x + 6) = 16\) years.

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20.

The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

Answer: B

As the ratio of their present ages is 3 : 4 , let their present ages be \(3x\)  and \(4x\) respectively.


So, 5 years ago, as the ratio of their ages was 5 : 7, we can write  \((3x-5) : (4x-5) = 5 : 7\)


 Solving, we get   \(x=10\)


Hence, their present ages are   \(3x = 30\)  and  \(4x=40\)

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