Test: Problems On Ages - 1 - GMAT MCQ

Let present age of P and Q be 3x
and  4x  respectively.
Ten years ago, P was half of Q's age

Total of their present ages
=3x+4x=7x=7×5=35

Assume that Sunil's present age 
= x.
Then, father's present age  =3x + x = 4x

After 8 years, father's age =  times of Sunils' age

After further  8  years,
Sunil's age  = x + 8 + 8 = 8 + 8 + 8 = 24
Father's age  = 4 x + 8 + 8 = 4 x 8 + 8 + 8 = 48

Father's age/Sunil's age = 48/24 = 2

• Let the present age of the man = y
• Man's age 10 years ago = (y-10)
• Man's age 10 years later = (y+10)

As mentioned in the question, 

• 125% of (y-10) = 250/3% of (y+10)
• 125/100 x (y - 10) = 250/3 x 1/100 x (y+10)

After Calculating, we get

• 5/4x(y-10) = 5/6 x (y+10)
• 6y - 60 = 4y +40
• 2y = 100
• y = 50
   

Let present age of the son = x years
Then, present age the man = ( x + 24 ) years

Given that, in 2 years, man's age will be twice the age of his son
⇒(x+24)+2=2(x+2)
⇒x=22

Ratio of the present age of Kiran and Syam = 5 : 4

Let present age of Kiran = 5x
Present age of Syam = 4x
After 3 years, ratio of their ages = 11 : 9
⇒ ( 5 x + 3 ) : ( 4 x + 3 ) = 11 : 9
⇒ 9 ( 5 x + 3 ) = 11 ( 4 x + 3 )
⇒ 45 x + 27 = 44 x + 33
⇒ x = 33 − 27 = 6
Syam's present age = 4 x = 4 × 6 = 24

Let the age of the youngest child = x
Then, the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 )
x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50
⇒ 5 x + 30 = 50
⇒ 5 x = 20

Let age of C = x .

Then, Age of B = 2x
Age of A = 2 + 2x
Total age of A,B and C =27

B's age =2x=2×5=10

Total age of all students 
= 22 × 21

Total age of all students + Age of the teacher  = 23 × 22

Let son's present age be x years. Then,

Son's age 5  years back = 19 − 5 = 14

Let Ayisha's present age = x
Then, her father's age = 6 x
Given that Ayisha's father's age will be twice Shankar's age after 10 years. Therefore, Shankar's age after 10 years

Also given that Shankar's eight birthdays was celebrated two years before. Therefore, Shankar's age after 10 years = 8 + 12 = 20

Therefore, Ayisha's present age =5 years