Problems on Ages Questions and Answers

Answer: B

C is 60 years old.

Let B's present age be b. Then C = 3b, and since C is 24 years younger than A, A = 3b + 24. Four years ago A was \(3b + 20\), which equals four times B's present age:

\[ \begin{aligned} 3b + 20 &= 4b \\ b &= 20 \end{aligned} \]

So B is 20, C is \(3 \times 20 = 60\), and A is 84. Check: four years ago A was 80, which is four times 20.

The other options fail this check; for example C = 54 gives B = 18 and A = 78, and 74 is not four times 18.

Answer: A

The equation is \(\frac{5}{6}(x - 5) - \frac{3}{5}(x - 8) = 6\).

Varun is x years old now, so Arun is x + 3. Eight years ago their ages were:

\[ \begin{aligned} \text{Arun} &= (x + 3) - 8 = x - 5 \\ \text{Varun} &= x - 8 \end{aligned} \]

Five-sixths of Arun's age then exceeded three-fifths of Varun's by 6, which is the first equation. The second swaps the two past ages, the third and fourth attach the fractions to the wrong person and use the wrong ages.

Answer: C

Raghav will be 46 years old. Let the ages five years ago be 3k and 5k. After 4 years from now (9 years after that date) their ages are 3k + 9 and 5k + 9, in the ratio 15 : 22. \[22(3k + 9) = 15(5k + 9)\] \[66k + 198 = 75k + 135\] \[9k = 63, k = 7\] Raghav's age five years ago was 35, so he is 40 now and 46 after 6 years. Check: Ajit is 26 now, and after 4 years the ages are 30 and 44, a ratio of 15 : 22.

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.

Answer: B

Let varun's age = \(x\) years.

From the given conditions,

\(\Rightarrow x+1 = 2(x-12)\)

\(\Rightarrow x=25\) years. 
 

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 

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.
 

Answer: C

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

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

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

So, \(x = 22\) 

Answer: D

Let Meena’s age = \(A\)

Then Sivagami’s age =  \(A+2\)

After 6 years the total of their ages will be 7 times of what?
Not clear.

So the given data are inadequate.

Answer: B

Let John's present age be  \(x\) 

\(\therefore \) \(x-5=\) \(\frac{1}{2}\left ( x+8 \right )\)

\(\Rightarrow \) \(x-5=\) \(\frac{1}{2}x +4\)

\(\Rightarrow \) \(\frac{1}{2}x=9\)

\(\Rightarrow \) \(x=18\)

Hence, John's is 18 years old.