## Problem Based on ages

#### Problem Based on ages

1. At present, the ratio between the ages of Gopal and Madhawa is 4 : 3. After 6 years, Gopal's age will be 26 years. The present age of Madhwa is:

1. Let the present age of Gopal and Madhawa are 4x and 3x years respectively.

##### Correct Option: C

Let the present age of Gopal and Madhawa are 4x and 3x years respectively; then
According to question,
4x + 6 = 26
⇒ 4x = 20
∴ x = 5
Hence, present age of Madhawa = 3x = 3 x 5 = 15 years

1. The sum of the ages of Ram, Shyam and Mohan is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. The present age of Mohan is:

1. Let us assume 10 years ago, ages of Ram, Shyam and Mohan were 2x, 3x and 4x years respectively.

##### Correct Option: A

Let us assume 10 years ago, ages of Ram, Shyam and Mohan were 2x, 3x and 4x years respectively.
Present ages of Ram, Shyam and Mohan will be 2x + 10 , 3x + 10 and 4x + 10 years.
According to question,
2x + 10 + 3x + 10 + 4x + 10 = 93
⇒ 9x + 30 = 93
⇒ 9x = 93 - 30
⇒ 9x = 63
⇒ x = 7
The present age of mohan = 4x + 10 = 4x7 + 10 = 38 years

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