The sum of the ages of a father and his son is 4 times the age of the son. If the average age of the father and the son is 28 years, What is the son's age?

Let l = 4k and b = 9k
Area of rectangle = l x b
144 = 4k x 9k
? k² = 144/36
? k² = 4
? k = 2
? l = 8 cm and b = 18 cm

Perimeter of rectangle = 2(l + b)
= 2(8 + 18)
= 2 x 26
= 52 cm

If the trains meet after t h.
Relative speed of train = (24 -18) = 6 km/h
? Distance = 27
? t = 27/6 = 9/2 h
? QR distance travel by train which is travelling at a speed of 18 km/h = 18t = 18 x 9/2 = 81 km

Let the number be a and b
Then, (a-b) = (a² - b²) / a+b
= 145/29
= 5

Let the four consecutive even number are x, ( x+2), (x+4), (x+6).
Clearly this is a series of consecutive even numbers
According to the formula,
Average of consecutive numbers = (first number + last number)/ 2
? 27 = [x + (x + 6)]/2
? x + 3 = 27
? x =24

? Greatest number = 4th consecutive even number = (x + 6) = 24 + 6 = 30

Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2

Total number of ways of selecting one number from 25 number is ²⁵C₁ ways.
Let E be the event of drawing a number divisible by both 2 and 3
i.e., (if a number is divisible by both 2 and 3, it is divisible by 6 also)
E = {6, 12, 18, 24}
? Required probability = P(E) = n(E) / n(S) = 4/25

Average = (0.64204 + 0.64203 + 0.64202 + 0.64201)/ 4
=2.5681/ 4
=0.642025