Problems on Ages Questions and Answers

Answer: D

Let, Ages of Vijaya and Simran – 1 year ago was  \(4A\) and \(A\) years respectively.

Then, \([(4A + 1) + 6] - [(A + 1) + 6] = 9\)

\(\Rightarrow3A = 9 \)

\(\Rightarrow A=3\)

Needed Ratio =   \((4A + 1) : (A + 1) = 13 : 4\)
 

Answer: A

Let the ages of children be \(x, (x + 3), (x + 6), (x + 9)\) and \((x+12)\) years

Then \(x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50\)

\(\Rightarrow \) \(5x=20\)

\(\Rightarrow\) \(x=4\)

\(\therefore \) Age of the youngest child \(=x=4\) 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 \(= 4x = 24 years\)

Answer: D

Let Anushka age = \(x \) years

Charu latha 12 yrs older than Anushka so Charu latha age =  \(x=12\)
Kajal is thrice as old as Anushka so Kajal age =  \(3x\)

The ages of Anushka, Kajal and Charu latha together are 57 years 

i.e , \( x + (x+12) + 3x = 57\)

\(\Rightarrow 5x = 45\)

\(\therefore x=9\)

Anushka age = 9
Kajal age =  \(3x = 27\)

Charu latha age = \(x+12 = 21\)

Answer: C

Mother's age when Ayesha's brother was born = 36 years

Father's age when Ayesha's brother was born = \((38 + 4)\) years = 42 years

\(\therefore \)  Required difference = \((42 - 36)\)years = 6 years

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.

Answer: A

Write the condition algebraically.

\[ A + B = (B + C) + 12 \]

The \( B \) cancels from both sides:

\[ A - C = 12 \]

So C is 12 years younger than A. B's age never matters - which is why it is not given.

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

Answer: C

Let the age of Sooraj and Vimal, 1 year ago, be  \(6x\) and  \(7x\) respectively

Given that, four years hence, this ratio would become 7:8

\(⇒ ( 6 x + 5 ) : ( 7 x + 5 ) = 7 : 8\)

\(⇒ 8 ( 6 x + 5 ) = 7 ( 7 x + 5 )\)

\(⇒ 48 x + 40 = 49 x + 35\)

\(⇒ x = 5 \)

Vimal's present age = \(7 x + 1 = 7 × 5 + 1 = 36 \) years

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