A man goes to the fair in Funcity with his son and faithful dog. Unfortunately man misses his son which he realises 20 minutes later. The son comes back towards his home at the speed of 20 m/min and man follows him at 40 m/min. The dog runs to the son (child) and comes back to the man (father) to show him the direction of his son. It keeps moving to and fro at 60 m/min between son and father, till the man meets the son. what is the distance travelled by the dog in the direction of the son?

Let son's age 10 years ago be x years.
? father's age 10 years ago = 3x years
? 3x + 20 = 2(x + 20)
? x = 20
? Ratio of their present ages = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3

Let the ages of Laxmi and her mother be 11x and 3x respectively.
From question, 11x - 3x = 24
? x = 3

? Ratio of their ages after 3 years = ( 3x + 3) : (11x + 3 )
= 12: 36 = 1 : 3

Let the respective ages of A, B and C, ten years ago be x, 2x and 3x years.
? (x + 10) + (2x + 10) + ( 3x + 10) = 90
? 6x = 60
? x = 10
? B's present age = 2x + 10 = 30 years

Let father's age be x years and the sum of ages of children be y years.
? x = 4 y ....(i)
Also (x + 6) = 2(y + 6 + 6 + 6) ....(ii) [6 is added thrice for three children ]

Solving (i) and (ii)
x = 60 years, and y = 15 years.

Let the Rahul's present age is 'A' years. Then Ritu's present age is (A + 8)
Now, according to the question,
(A + 8) - 3 = x
? A = (x - 5) years

Let the present age of A and B be x and y years respectively

From 1st condition
(x - 1) / (y -1) = 3/4
? 4x - 4 = 3y - 3
? 4x - 3y = 1 ... (i)

From 2nd condition,

(x + 1) / (y + 1) = 5/6
? 6x + 6 = 5y + 5
? 6x - 5y = -1 ...(ii)

Multiplying equation (i) by 3 and equation (ii) by 2 and subtract
y = 5
? Present age of B = 5 years

Let the present age of father be x years, Then the present age of son = (x - 25) years .

According to to question,
x - 4 = 45
? x = 45 + 4
? x = 49
? Age of son = 49 - 25 = 24 years
? Age of son after five years = 24 + 5 = 29 years

? Age of father after five years = 49 + 5= 54 years
Total age of both = 29 + 54= 83 years

Let 10 yr ago, ages of Ram and Rahim were k yr and 3k yr, respectively.
Then, present age of Ram = (k + 10)
and present age of Rahim = (3k + 10)
According to the question, (k + 10 + 5) / (3k + 10 + 5) = 2/3
? 3k + 45 = 6k + 30
? 3k = 15
? k = 5
Hence, required ratio = (5 + 10) / (3 x 5 + 10)
= 15/25
= 3 : 5

Let present age of Ravi be k.
Then, Present age of Ravi's father = 4k.
Now, 5 yr ago,
Ravi's father's age = 7 x Ravi's age
? 4k - 5 = 7(k - 5)
? 4k - 5 = 7k - 35
? 3k = 30
? k = 10
? Ravi's present age = k = 10 yr
? Ravi's father's present age = 4k
= 4 x 10 = 40 yr

Let the age of Mr Manoj be (10y + y) yrs.
? His wife's age = (10y + x ) years

Then, ((10x + y + 10y + x) / 11 = 10x + y -10y-x
? x + y = 9x - 9y
? 8x = 10y
? x/y = 5/4

? x = 5 and y =4 (because any other multiple of 5 will make x of two digits).
? Diff. = (10x + y) - (10y - x)
= 9x - 9y
= 9(x-y)
= 9(5-4)
= 9 yrs.