As per the given details in question, we have
Sum of the present age of P, Q and R = (25 × 3 + 3 × 5) years
Sum of the present age of P, Q and R = (75 + 15) years = 90 years
Sum of the present age of Q and R = (20 × 2 + 2 × 7) years
Sum of the present age of Q and R = 54 years
∴ p’s present age = Sum of the present age of P, Q and R - Sum of the present age of Q and R

Correct Option: A

As per the given details in question, we have
Sum of the present age of P, Q and R = (25 × 3 + 3 × 5) years
Sum of the present age of P, Q and R = (75 + 15) years = 90 years
Sum of the present age of Q and R = (20 × 2 + 2 × 7) years
Sum of the present age of Q and R = 54 years
∴ p’s present age = Sum of the present age of P, Q and R - Sum of the present age of Q and R
Hence , p’s present age = (90 – 54) years = 36 years

Here , The average age of 9 students and teacher = 16 years
Total age of 9 students and teacher = 16 × 10
The average age of the first four students = 19 years
Total age of the first four students = 19 × 4
And the average age of the last five students = 10 years
Total age of the last five students = 5 × 10
∴ Teacher’s age = 16 × 10 – 19 × 4 – 5 × 10

Correct Option: B

Here , The average age of 9 students and teacher = 16 years
Total age of 9 students and teacher = 16 × 10
The average age of the first four students = 19 years
Total age of the first four students = 19 × 4
And the average age of the last five students = 10 years
Total age of the last five students = 5 × 10
∴ Teacher’s age = 16 × 10 – 19 × 4 – 5 × 10
Teacher’s age = 160 – 76 – 50 = 34 years

Here , The average age of a father and a mother = 35 years
Total age of ( Father + mother ) = 2 × 35 = 70 years
The average age of father , mother and son = 27 years
Total age of ( Father + mother + son ) = 27 × 3 = 81 years

Correct Option: B

Here , The average age of a father and a mother = 35 years
Total age of ( Father + mother ) = 2 × 35 = 70 years
The average age of father , mother and son = 27 years
Total age of ( Father + mother + son ) = 27 × 3 = 81 years
∴ Son’s age = 81 – 70 = 11 years

Given that , 5 years ago, the average age of A, B, C and D = 45
years.
Sum of A, B, C and D = 45 × 4 = 180 years
Sum of the present age of A, B, C and D = 45 × 4 + 4 × 5 = 180 + 20 = 200 years
With E joining them now, the average age of A, B, C , D and E = 49 years.
Sum of the present age of A, B, C, D and E = 49 × 5 = 245 years
∴ Present age of E = Sum of the present age of A, B, C, D and E - Sum of the present age of A, B, C and D

Correct Option: C

Given that , 5 years ago, the average age of A, B, C and D = 45
years.
Sum of A, B, C and D = 45 × 4 = 180 years
Sum of the present age of A, B, C and D = 45 × 4 + 4 × 5 = 180 + 20 = 200 years
With E joining them now, the average age of A, B, C , D and E = 49 years.
Sum of the present age of A, B, C, D and E = 49 × 5 = 245 years
∴ Present age of E = Sum of the present age of A, B, C, D and E - Sum of the present age of A, B, C and D
∴ Present age of E = (245 – 200) years = 45 years

Here , Age of replaced boy = 10 years
Total age increase = 2 × 24 = 48 months = 4 years
∴ Age of the new boy = Age of replaced boy + Total age increase

Correct Option: C

Here , Age of replaced boy = 10 years
Total age increase = 2 × 24 = 48 months = 4 years
∴ Age of the new boy = Age of replaced boy + Total age increase
Hence , Age of the new boy = 10 + 4 = 14 years.