## Problem Based on ages

#### Problem Based on ages

1. The age of Shyam is 1/3 rd that of his mother. He is 2 years older than his sister. The age of his sister be 8 years, what is the age of his mother?

1. Given that :- Age of Shyam’s sister = 8 years
Age of Shyam = 2 + 8 = 10 years
Suppose the age of Shyam’s mother = P
According to question

 Age of Shyam' s mother × 1 = Age of Shyam 3

 P = 10 3

##### Correct Option: D

Given that :- Age of Shyam’s sister = 8 years
Age of Shyam = 2 + 8 = 10 years
Suppose the age of Shyam’s mother = P
According to question

 Age of Shyam' s mother × 1 = Age of Shyam 3

 P = 10 3

∴ P = 3 × 10 = 30 years
Hence , age of Shyam’s mother is 30 years .

1. Ramu is 48 years old. Robin is 6 years junior to Ramu and 14 years senior to Rohit. Ramu has two children – Neethu and Vinu. Youngest sister of Rohit is Krishna and she is 15 years junior to him. So what is the age of Krishna?

1. According to question ,
Given :- Age of Ramu = 48 years
Age of Robin = Age of Ramu - 6 years = 48 – 6 = 42 years
Age of Rohit = Age of Robin - 14 years = 42 – 14 = 28 years
Age of Krishna = Age of Rohit - 15 years = 28–15 =13 years

##### Correct Option: A

According to question ,
Given :- Age of Ramu = 48 years
Age of Robin = Age of Ramu - 6 years = 48 – 6 = 42 years
Age of Rohit = Age of Robin - 14 years = 42 – 14 = 28 years
Age of Krishna = Age of Rohit - 15 years = 28–15 =13 years
Hence , Age of Krishna is 13 years .

1. The average age of 30 students is 15 years. If the teacher’s age is also included then the average age increases by 1 year. The age of the teacher is

1. According to question ,
The average age of 30 students = 15 years
Total age of 30 students = 30 × 15 = 450 years
Total age of 30 students and teacher = ( 15 + 1 ) × 31 = 496 years
∴ Age of teacher = Total age of 30 students and teacher - Total age of 30 students

##### Correct Option: B

According to question ,
The average age of 30 students = 15 years
Total age of 30 students = 30 × 15 = 450 years
Total age of 30 students and teacher = ( 15 + 1 ) × 31 = 496 years
∴ Age of teacher = Total age of 30 students and teacher - Total age of 30 students
Age of teacher = ( 496 – 450 ) = 46 years

1. A was born 5 years before B, B is 4 years older than C and 3 years younger to D. If A is now 17 years old, how old is D?

1. Here , Present age of A = 17 years
Age of B = age of A - 5 years = 17 – 5 = 12 years
Age of C = age of B – 4 years =12 – 4 = 8 years

##### Correct Option: B

Here , Present age of A = 17 years
Age of B = age of A - 5 years = 17 – 5 = 12 years
Age of C = age of B – 4 years =12 – 4 = 8 years
Age of D = Age of B + 3 years =12 + 3 = 15 years

1. Ashok’s mother was 3 times as old as Ashok 5 years ago. After 5 years she will be twice as old as Ashok. How old is Ashok today?

1. Suppose the present age of Ashok is P years and that of his mother is Q years.
5 years ago 3 ( P – 5 ) = ( Q – 5 )
⇒ 3P – 15 = Q – 5

##### Correct Option: B

Suppose the present age of Ashok is P years and that of his mother is Q years.
5 years ago ,
3 × ( age of Ashok - 5 ) = ( age of Ashok 's mother - 5 )
3 ( P – 5 ) = ( Q – 5 )
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 ....(i)
5 years after,
2 × ( age of Ashok + 5 ) = ( age of Ashok '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
Hence , the present age of Ashok is 15 years .