Problems on Ages Questions and Answers

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

Answer: C

Let age of Sunil = \(x \) years and age of syam be = \(y\) years

\(x y = 240 ⋯ ( 1 )\)

\(2 x = y + 4\)

\(⇒ y = 2 x − 4\)

\(⇒ y = 2 ( x − 2 ) ⋯ ( 2 )\)

Substituting equation \((2)\) in equation \((1)\) we get , 

\(x × 2 ( x − 2 ) = 240\)

\(⇒ x ( x − 2 ) = \) \(\frac{240}{2}\)

\(⇒ x ( x − 2 ) = 120 ⋯ ( 3 )\)

We got a quadratic equation to solve.

Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. 
But it is more easy to substitute the values given in the choices in the quadratic equation (equation 3) and see which choice satisfy the equation.

Here, option A is 10. If we substitute that value in the quadratic equation, 

\(x ( x − 2 ) = 10 × 8\) which is not equal to 120

Now try option B which is 12. If we substitute that value in the quadratic equation, 
\(x ( x − 2 ) = 12 × 10 = 120 \)  See, we got that  \(x=12\)\

Hence Sunil's age = 12
 

Answer: D

otal ages of 80 boys = 15 x 80 = 1200 yrs.
Total age of 16 boys = 15 x 16 = 240 yrs
Total age of 25 boys = 14 x 25 = 350 yrs.
Average age of remaining boys = \(1200 - \frac{240+350}{80}-\left ( 25+15 \right )\)=  \(\frac{610}{41}\)

= 15.25 yearss

Answer: C

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.