Let the ages of A and B are 4N and 5N yr. respectively.
According to the question,
∴ (4N + 4)/(5N + 4) = 14/17

Correct Option: A

Let the ages of A and B are 4N and 5N yr. respectively.
According to the question,
∴ (4N + 4)/(5N + 4) = 14/17
⇒ 68N + 68 = 70N + 56
⇒ 2N = 12
⇒ N = 6
Hence present age of B = 5 x 6 = 30 yr

∵ Total age of 8 children = 8 x 12 = 96 yr
And total age of 7 children = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82

Correct Option: B

∵ Total age of 8 children = 8 x 12 = 96 yr
And total age of 7 children = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82
∴ The age of 8th child = 96 - 82 = 14 yr

Let father's age be 4T and son's age T years.
∵ 4T x T = 196

Correct Option: C

Let father's age be 4T and son's age T years.
∵ 4T x T = 196
⇒ T² = 49
∴ T = 7
Father's age after 5 years = (4T + 5) = 33 years
Son's age after 5 years = (T + 5) = 12 years
∴ Ratio of their ages after 5 years = 33 : 12 = 11 : 4

Length of the train = 280 m
Length of the platform = 280 x 3 = 840 m
Taken time = 6 min 40 s = (360 + 40) s = 400 s
∴ Required speed = Distance / Time

Correct Option: C

Length of the train = 280 m
Length of the platform = 280 x 3 = 840 m
Taken time = 6 min 40 s = (360 + 40) s = 400 s
∴ Required speed = Distance / Time = (840 + 280)/400
= 1120/400 = 2.8 m/s

Let my present age be x years.
∵ x - 20 = x / 3

Correct Option: A

Let my present age be x years.
∵ x - 20 = x / 3
⇒ 3x - 60 = x
⇒ 2x = 60
∴ My present age = x = 30 years