Problems on Ages Questions and Answers

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21.

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?

A.56 years
B.62 years
C.66 years
D.72 years

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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22.

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 ?

A.50 years
B.60 years
C.70 years
D.80 years

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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23.

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).

A.8, 20, 28
B.16, 28, 36
C.20, 35, 45
D.None of these

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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24.

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 ?

A.44 years
B.48 years
C.54 years
D.58 years

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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25.

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

A.34,11
B.35,10
C.36,9
D.40,5

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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26.

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?

A.16 years
B.18 years
C.20 years
D.Cannot be determined
E.None of these

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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27.

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.

A.20,30
B.30,40
C.40,50
D.35,45

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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28.

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 ?

A.30 years
B.36 years
C.42 years
D.48 years

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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29.

The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest

A.18 years
B.19 years
C.20 years
D.21 years

Answer: C

Present total age of the members = 26(5) = 130 years

Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 - 10 = 120 years

Their average age at the time of the birth of the youngest member = \(\frac{120-(4*10)}{4}\)

= 30 - 10 = 20 years

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30.

Rohit is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Rohit

A.31.5 years
B.32.5 years
C.22.5 years
D.24.5 years

Answer: D

lets Rahul's age is \(x\) years

Then Rohit's age \(=(x-7)\) years

so, \(\frac{(x-7)}{x}=\frac{7}{9}\)

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

\(\Rightarrow\) \(2x=63\)

\(\Rightarrow\) \(x=31.5\)

\(\therefore \) Rohit's age \(31.5-7=24.5\) years

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