Problems On AgesPage 1
1.  Rohan's age after 15 years will be 5 times his age 5 years back. What is the present age of Rohan?  (a)8 years  (b)9 years  (c)10 years  (d)11 years 

Answer is: CLet Rohan's present age be X years. Then,
Rohan's age after 15 years = (X + 15) years
Rohan's age 5 years back = (X  5) years
∴ X + 15 = 5(X  5)
⇒ X + 15 = 5X  25
⇒ X = 10.
Hence, Rohan's present age = 10 years.
2.  The age of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, Find their present ages.  (a)14, 30  (b)15, 31  (c)16, 32  (d)17, 33 

Answer is: ALet the age of the younger person be X years.
Then, age of the elder person = (X+16) years.
∴ 3(X  6) =(X + 16  6)
⇒ 3X – 18 = X + 10
2X = 28
X = 14
Hence, their present ages are 14 years and 30 years.
3.  The product of the ages of Ankit and Nitin is 240. If twice the age of Nitin is more than Ankit's age by 4 years, what is Nitin's age?  (a)11 years  (b)12 years  (c)13 years  (d)14 years 

Answer is: BLet Ankit's age be X years. Then Nitin's age = 240/X years.
∴ 2 x 240/X X = 4
⇒ 480  X² = 4X
X² + 4X 480 = 0
⇒(X + 24)(X  20) = 0
⇒ X = 20
Hence, Nitin age =(240/20) years = 12 years.
4.  The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.  (a)30 years  (b)31 years  (c)32 years  (d)33 years 

Answer is: DLet the son's present age be X years. Then, father's present age = (3X +3)years
∴(3X+3+3) = 2(X+3)+10
3X + 6 = 2X + 16
X= 10
Hence, Father's present age = (3X+3) = (3 x10 + 3) = 33 years
5.  Sohit was 4 times as old as his old as his son 8 years ago. After 8 years, Sohit will be twice as old as his son. What are their present ages?  (a)30 years  (b)35 years  (c)40 years  (d)45 years 

Answer is: CLet son's age after 8 years ago be X years. Then, Sohit's are 8 years ago = 4X years.
Son's age after 8 years =(X+8)+8 =(X+16) years.
Sohit's age after 8 years =(4X+8)+8 =(4X+16)years.
∴ 2(X+16) = 4X+16
X = 8 years.
Hence, son's present age =(X+8) = 8+8 = 16
Sohit's present age = 4X+8 = 32+8 = 40 years.
6.  A years ago, the ratio of Gourav's and Sachin's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Sachin ?  (a)35 years  (b)36 years  (c)37 years  (d)38 years 

Answer is: BLet Gaurav's and Sachin's age one years be 6X and 7X years respectively. Then,
Gaurav's age 4 years hence = (6X+1) + 4 = (6X + 5) years
Sachin's age 4 years hence = (7X+1) + 4 = (7X + 5) years
∴ (6X + 5)/(7X + 5) = 7/8
⇒ 8(6X + 5) = 7(7X + 5)
⇒ 48X + 40 = 49X + 35
⇒ X = 5
Hence, Sachin's present age = 7X+1 = 36 years
7.  Abhay's age after six years will be three seventh of his father's age. Ten years ago, the ratio of their ages was 1 : 5. What is father's age at present?  (a)30 years  (b)40 years  (c)50 years  (d)60 years 

Answer is: CLet the ages of Abhay and his father 10 years ago be X and 5X years respectively. Then,
Abhay's age after 6 years = (X+10) + 6 =(X+16) years
Father's age after 6 years = (5X+10) + 6 = 5X+16 years
∴(X+16) = 3/7(5X+16)
⇒ 7(X+16) = 3(5X+16)
⇒ 7X + 112 = 15X + 48
⇒ 8X = 64
⇒ X = 8
Hence, Abhay's father's present age =(5X+10) = 50 years
8.  The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 4 : 5. What is the present age of Saransh?  (a)37 years  (b)38 years  (c)39 years  (d)40 years 

Answer is: BLet the ages of Jayant, Prem and Saransh 10 year ago be 2X,3X and 4X years respectively.
Then,(2X+10) + (3X+10) + (4X+10) = 93
⇒ 9X = 63
⇒ X = 7
∴ Saransh's present age =(4X+10) = 38 years