Test: Problems on Ages - 3 - GMAT MCQ

Let the present age of the son = x Then, present age of the father = ( 60 − x ) Six years ago father's age was 5 times the age of the son

Son's age after 6 years = x + 6 = 14 + 6 = 20

Let age of Kiran and Bineesh be 7x and  9x  respectively

Kiran's age = 7 x = 7 × 3.5 = 24.5

Given that, six years ago, the ratio of the ages of Vimal and Saroj = 6 : 5
Hence we can assume that age of Vimal six years ago = 6x
age of Saroj six years ago = 5x
After 4 years, the ratio of their ages = 11 : 10

Saroj's present age

= ( 5x + 6 ) = 5 x 2 + 6 = 16

After 6 years, Shekhar's age will be 26 years
Therefore, Present age of Shekhar = 26 − 6 = 20
Let present age of Shobha = x

Let my age = x
Then
My brother's age = x + 3
My mother's age = x + 26
My sister's age = ( x + 3 ) + 4 = x + 7 My father's age = ( x + 7 ) + 28 = x + 35
Age of my father when my brother was born = x + 35 − ( x + 3 ) = 32

Let present age of A,B and C be 4 x , 7 x and 9 x respectively.
(4x−8)+(7x−8)+(9x−8)=56
⇒20x=80
⇒x=4
Hence present age of A, B and C are
4 × 4 , 7 × 4 and 9 × 4 respectively.
i.e., 16 , 28 and 36 respectively.

Let present age of the person =x
Then, present age of the mother = 5x/2
Given that, after  8  years, the person will be one-half of the age of his mother.


 

Age of C < Age of A < Age of B

Given that sum of the ages of B and C is 50 years.

Now we need to find out (B's age - A's age). But this cannot be determined with the given data.

Let Sobha's age = x and
her brother's age = x − 4
Sobha's father's age = x + 38
Sobha's mother's age = ( x − 4 ) + 36 = x + 32
Sobha's father's age - Sobha's mother's age
=(x+38)−(x+32)=6

Let age of the son before 10 years = x and  age of the father before 10 years = 3 x
(3x + 20 ) = 2 ( x + 20 )
⇒ x = 20
Age of the son at present = x + 10 = 20 + 10 = 30
Age of the father at present = 3 x + 10 = 3 × 20 + 10 = 70
Required ratio = 70 : 30 = 7 : 3

Let present age of the elder person = x and
present age of the younger person = x − 16

Let the present age the son = x

Then, present age of the father = 3 x + 3

Given that, three years hence, father's age will be 10 years more than twice the age of the son

⇒ ( 3 x + 3 + 3 ) = 2 ( x + 3 ) + 10

⇒ x = 10

Father's present age

= 3 x + 3 = 3 × 10 + 3 = 33

Let age of the son before 8 years = x

Then, age of Kamal before 8 years ago = 4x

After 8 years, Kamal will be twice as old as his son

⇒ 4 x + 16 = 2 ( x + 16 )

⇒ x = 8

Present age of Kamal = 4 x + 8 = 4 × 8 + 8 = 40

Present age of Denis = 5 years

Present age of Rahul = 5 − 2 = 3

Let present age of Ajay = x

Then, present age of Rahul 

Let the present age of the man and his wife be 4 x and 3 x respectively.

After 4 years this ratio will become 9 : 7 ⇒ ( 4 x + 4 ) : ( 3 x + 4 ) = 9 : 7
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8

Present age of the man = 4 x = 4 × 8 = 32
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24

Let age of Sunil = x
and age of Syam = y
xy = 240 ⋯ ( 1 )

Substituting equation ( 2 ) in equation ( 1 ) . We get

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
(Or else, we can solve the quadratic equation by factorization as,

Since x is age and cannot be negative, x = 12
Or by using quadratic formula as


Since age is positive, x = 12

Let the age of Sooraj and Vimal, 1 year ago, be 6 x and 7 x respectively.
Given that, four years hence, this ratio would become 7 : 8

Given that, A + B = 12 + B + C

⇒ A - C = 12

Therefore, C is younger than A by 12 years

Let present age of Sachin = x . Then,
( x + 15 ) = 5 ( x − 5 )
⇒ 4 x = 40
⇒ x = 10

Let the age of Sandeep and his father before 10 years be x and 5 x respectively.
Given that Sandeep's age after six years will be three-seventh of his father's age

Sandeep's father's present age
= 5 x + 10 = 5 × 8 + 10 = 50