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Problems on Ages Questions and Answers

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41.

Present ages of Pritam and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?

Answer: A

Let the present ages of Pritam and Anand be \(5x\) years and \(4x\) years respectively.

Then, \(\frac{5x+3}{4x+3} =\frac{11}{9}\)

\(\Rightarrow\) \(9(5x + 3) = 11(4x + 3)\)

\(\Rightarrow 45x + 27 = 44x + 33\)

\(\Rightarrow 45x - 44x = 33 - 27\)

\(\Rightarrow x=6\)

\(\therefore\)  Anand's present age \(=4x=24\) years

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42.

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?

Answer: D

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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43.

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

Answer: A

Let the son's present age be \(x\) years. Then, \((38 - x) = x\)

\(\Rightarrow 2x = 38\)

\(\Rightarrow x=19\)

\(\therefore\) Son's age 5 years back \((19 - 5) = 14\) years.

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44.

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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45.

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:

Answer: D

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

\(\therefore (x + 24) + 2 = 2(x + 2)\)

\(\Rightarrow x + 26 = 2x + 4\)

\(\Rightarrow x = 22\)

 

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46.

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

Answer: A

Let the present ages of Sameer and Anand be \(5x\)years and  \(4x\)years respectively.

 

then \(\frac{5x+3}{4x+3}= \frac{11}{9}\)

\(\Rightarrow\) \(9\left ( 5x+3 \right )=11\left ( 4x+3\right )\)

\(\Rightarrow\) \(45x+27=44x+23\)

\(\Rightarrow \) \(45x - 44x = 33 - 27\)

\(\Rightarrow \) \(x = 6.\)

\(\therefore \) Anand's present age \(= 4x = 24 years\)

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47.

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

Answer: A

Let the son's present age be \(x \) years . 

Then, \(\left ( 38-x \right )=x\)

\(\Rightarrow \) \(2x=38 \)

\(\Rightarrow x=19 \)

\( \therefore \)  Son's age 5 years back (19-5) = 14 years

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48.

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

Answer: D

Let the present ages of son and father be \(x\) and \((60-x)\) years respectively 

Then ,   \((60-x)-6=5(x-6)\)

\( \Rightarrow \)  \(54 - x=5x-30\)

\( \Rightarrow 6x=84\)

\( \Rightarrow x=14 \)

 \( \therefore \) Son's age after 6 years = \(( x+ 6)\)= 20 years

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49.

At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

Answer: B

Let the present ages of Arun and Deepak be \(4x\) years and \(3x\) years respectively . Then ,

\(4x+6=26\)

\( \Rightarrow 4x=20\)

\(\therefore x=5\)

Now, Deepak's age  =  \(3x\) =  15

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50.

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

Answer: C

Let Rahul's age be \(x \) years .

Then, Sachin's age =  \((x-7)\) years

\(\therefore \) \(\frac{x - 7}{x}=\frac{7}{9}\)

\(\Rightarrow 9x - 63 = 7x\)

\(\Rightarrow 2x = 63\)

\(\Rightarrow x = 31.5\)

Hence, Sachin's age = \((x-7)\) = 24.5 years

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