Problems on Ages Questions and Answers

Q: 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 ?

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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51.

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:

A.12 years
B.14 years
C.18 years
D.20 years

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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52.

The ages of Krish and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:

A.10
B.13
C.15
D.18

Answer: C

Let Krish's age be \(3A\) and Vaibhav's age be \(5A\)

\(\therefore(3A+9)/(5A+9) = 3/4\)

\(\Rightarrow 4 (3A + 9) = 3 (5A + 9) \)

\(\Rightarrow A=3\)
Therefore, Vaibhav’s age = 15 years.

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53.

Rahul's age after 15 years will be 5 times his age 5 years back, What is the present age of Rahul?

A.8
B.10
C.12
D.14

Answer: B

Let Rahul's present age is \(x\) years.

Then \(x+15=5(x-5)\)

\(\Rightarrow\) \(4x=40\)

\(\Rightarrow\) \(x=10\)

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54.

Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age

A.12,28
B.14,30
C.16,32
D.18,34

Answer: B

Let the age of younger person is \(x\)

Then elder person age is \((x+6)\)

so 6 years before

\(3(x-6) = (x+16-6)\)

\(\Rightarrow\) \((3x-18) =( x+10)\)

\(\Rightarrow\) \(x=14\)

So other person age is \(x + 16 = 30\)

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55.

The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years

A.7:8
B.7:9
C.3:8
D.5:8

Answer: A

Let P age and Q age is \(6x\) years and \(7x\) years respectively

Then, \(7x-6x=4\)

\(\Rightarrow\) \(x=4\)

So required ratio will be \((6x+4): (7x+4)\)

\(\Rightarrow\) \(28:32\)

\(\Rightarrow 7:8\)

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56.

A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?

A.45,10
B.10,45
C.9,50
D.50,9

Answer: C

Let the age of A = \(A\), B = \(B\) and C = \(C\)

From given,

\(A = 3B\)

4 years ago,

\(A + 4 = 31\)

\(\Rightarrow A=27\)

sub in above \(B\) , we get \(B\) = 9

\(C = 2(27 - 4) + 4 = 46 + 4 = 50 \)

Hence B = 9years and C = 50years.

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57.

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?

A.24
B.27
C.32
D.40

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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58.

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 ?

A.2 years
B.3 years
C.4 years
D.5 years

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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59.

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]

A.4:3
B.12:11
C.7:4
D.6:5

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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60.

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?

A.13
B.14
C.15
D.16

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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