## Problem Based on ages

#### Problem Based on ages

1. Hari is twice as old as Johnny, who is three years older than Rahul. If Hari’s age is five times Rahul’s age, how old is Johnny?

1. Suppose the age of Johnny is P years and that of Rahul is Q years.
According to question ,
Age of Hari = 2 × Age of Johnny = 2P
And age of Hari = 5 × Age of Rahul = 5Q
⇒ 2P = 5Q
⇒ 2P – 5Q = 0 ........(i)
Again age of Johnny = Age of Rahul + 3 years
⇒ P = 3 + Q
⇒ P – Q = 3........ (ii)

##### Correct Option: C

Suppose the age of Johnny is P years and that of Rahul is Q years.
According to question ,
Age of Hari = 2 × Age of Johnny = 2P
And age of Hari = 5 × Age of Rahul = 5Q
⇒ 2P = 5Q
⇒ 2P – 5Q = 0 ........(i)
Again age of Johnny = Age of Rahul + 3 years
⇒ P = 3 + Q
⇒ P – Q = 3........ (ii)
On solving equations (i) and (ii), we get
Q = 2
∴ Age of Johnny = 3 + Q = 3 + 2 = 5 years
Hence , the age of Johnny is 5 years .

1. In a family, mother’s age is twice that of daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father?

1. Suppose the age of daughter is P years.
Age of brother = age of daughter + 5 years = P + 5 years
Age of mother = 2 × age of daughter = 2P years
According to question ,
∴ Age of mother - 20 years = Age of brother
⇒ 2P – 20 = P + 5
⇒ 2P – P = 5 + 20

##### Correct Option: B

Suppose the age of daughter is P years.
Age of brother = age of daughter + 5 years = P + 5 years
Age of mother = 2 × age of daughter = 2P years
According to question ,
∴ Age of mother - 20 years = Age of brother
⇒ 2P – 20 = P + 5
⇒ 2P – P = 5 + 20
⇒ P = 25 years
Age of mother = 2P = 2 × 25 = 50 years
Age of father = Age of mother + 10 years = 50 + 10 = 60 years

1. Ashu’s mother was three times as old as Ashu 5 years ago. After 5 years she will be twice as old as Ashu. How old is Ashu today?

1. Suppose the present ages of Ashu and her mother be P and Q years respectively.
According to question,
5 years ago , 3 × ( ages of Ashu - 5 ) = ages of Ashu's mother - 5
⇒ 3 ( P - 5 ) = Q - 5
⇒ 3P - 15 = Q - 5

##### Correct Option: D

Suppose the present ages of Ashu and her mother be P and Q years respectively.
According to question,
5 years ago , 3 × ( ages of Ashu - 5 ) = ages of Ashu's mother - 5
⇒ 3 ( P - 5 ) = Q - 5
⇒ 3P - 15 = Q - 5
⇒ 3P - Q = 10 ... (i)
Again, After 5 years , 2 × ( ages of Ashu + 5 ) = ages of Ashu's mother + 5
⇒ 2(P + 5) = Q + 5
⇒ 2P + 10 = Q + 5
⇒ 2P – Q = - 5.... (ii)
From equations (i) and (ii) , we get
P = 15 years
Therefore, Ashu is 15 year old at present.

1. Father is 5 years older than mother and mother’s age now is thrice the age of the daughter. The daughter is now 10 years old. What was the father’s age when the daughter was born?

1. Here , Father = F , Mother = M and Daughter = D
According to question
Age of F = Age of M + 5,
Age of M = 3 × Age of D and Age of D = 10 years
∴ Age of M = 3 × 10 = 30 years

##### Correct Option: C

Here , Father = F , Mother = M and Daughter = D
According to question
Age of F = Age of M + 5,
Age of M = 3 × Age of D and Age of D = 10 years
∴ Age of M = 3 × 10 = 30 years
Therefore, father’s present age = 30 + 5 = 35 years
Required answer = father’s present age - 10 years = 35 – 10 = 25 years

1. The age of Ram is double that of Shyam and half the of Sohan. Shyam is older than Mohan. Who is the oldest?

1. Suppose the age of Shyam = P years
According to question ,
Age of Ram = 2 × age of Shyam = 2P years
Age of Sohan = 4 × age of Shyam = 4P years

##### Correct Option: C

Suppose the age of Shyam = P years
According to question ,
Age of Ram = 2 × age of Shyam = 2P years
Age of Sohan = 4 × age of Shyam = 4P years
∴ Shyam > Mohan
So, Sohan (4P) > Ram (2P) > Shyam (P) > Mohan
∴ Sohan is the oldest.