Let us assume the present age of Ram R, Shyam S and Mohan M.

Correct Option: A

Let us assume the present age of Ram R, Shyam S and Mohan M.
5 years ago, Ram age = R - 5
5 years ago, Shyam age = S - 5
5 years ago, Mohan age = M - 5
According to question,
5 years ago, the average age of Ram and Shyam was 20 years,
(5 years ago, Ram age + 5 years ago, Shyam age) /2 = 20
(R - 5 + S - 5 )/2 = 20
R + S = 40 + 10 = 50 ................(1)
Now Again according to question,
Now , the average age of Ram, Shyam and Mohan is 30 years
(R + S + M)/3 = 30
R + S + M = 90
Pu the value of R + S from equation (1)
50 + M = 90
M = 90 - 50 = 40
The present age of Mohan = 40 years
10 years hence, the age of Mohan = 40 + 10 = 50 years

Let us assume the present ages of Suresh and his daughter be 2x and x years respectively.

Correct Option: B

Let the present ages of Suresh and his daughter be 2x and x years respectively; then
According to question,
Six years hence, the ratio of their ages would be 23 : 13
(2x + 6) / (x + 6) = 23/13
⇒ (2x + 6) 13 = 23 (x + 6)
⇒ 26x + 78 = 23x + 138
⇒ 3x = 60
∴ x = 20
Hence, present age of Suresh = 2 x 10 = 40 years

Let us assume the present ages of son be Y then his father present age will be Y + 34 years.

Correct Option: B

Let us assume the present ages of son be Y then his father present age will be Y + 34 years. then
12 years ago, father's age = Y + 34 -12
12 years ago, Son's age = Y - 12
Now according to question,
12 years ago, father's age was 18 times the age of his son. then
18( Y - 12 ) = Y + 34 - 12
⇒ 18Y - 216 = Y + 22
⇒ 17Y = 238
∴ Y = 14
Hence, present age of his son = 14 years.

Let the present ages of two person be 4x and 7x years respectively;

Correct Option: B

Let the present ages of two person be 4x and 7x years respectively; then according to question,
7x = 30 + 4x
⇒ 3x = 30
∴ x = 10
Hence, sum of their ages = 4x + 7x = 11x = 11 x 10 = 110 years

Let us assume the age of second son be Y, then age of first son will be Y + 10 and age of father will be (Y + 10 + 30) years respectively;

Correct Option: C

Let us assume the age of second son be Y, then age of first son will be Y + 10 and age of father will be (Y + 10 + 30) years respectively;
then according to question,
sum of their ages be 95 years.
x + x + 10 + x + 10 + 30 = 95
⇒ 3x = 95 - 50
⇒ 3x = 45
∴ x = 15
age of the father = x + 10 + 30
Hence, age of the father = 15 + 10 + 30 = 55 years.