A 280 m long train crosses a platform which is three times of its length, in 6 min 40 s. What is the speed of the train?

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

Let B;s age 2 years ago be N years
? A's present age = 2N years

From question, 2N - (N + 2) = 2
? N = 4
? A's age = 2 x 4 = 8 years

Let the age of A be (x - 3) years
? B's age = x years
? C's age = (x - 3) + 2 = x - 1
? B's age - C's age = x - (x - 1) = 1 year
? B is one year older then C.

Suppose x years later the father will be twice as old as his son.
? x + 41 = 2 (x + 16)
? x = 41 - 32 = 9 years

Let the age of B be N years
According to the question
? N + 20 = 6N
? N = 4 years
? A's age = 4 x 6 = 24 years and B's age = 4 years

Required ratio = (36 - 8)/(24 - 8) = 28/16 = 7 : 4

? 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 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

Let present ages of indira and Lizzy are 3k yr and 8k yr, respectively.
? 3k + 8 = 20 ? 3k = 12
? k = 4
Hence, Lizzy's required age = 8k - 5
= 32 - 5
= 27 yr

Let 7 yr ago, ages of A and B 4k yr and 5k yr, respectively.
Then, present age of A = 4k + 7
and present age of B = 5k + 7
Now, according to the question,
? (4k + 7 + 7) / (5k + 7 + 7) = 5/6
? 24k + 84 = 25k + 70
? k = 14
Hence, B's present age = 5 x 14 + 7 = 77 yr