Questions

Let speed of train B be x m/s And length of train B be y m
Then length of train A is 2y m
Speed of train A = 84 × 5/18 = 210/9 m/s = 70/3 m/s
A.T.Q, (2y+y)/10 = 70/3 − x .............(i)
and (2y+y)/ 22.5 = 70/3 − 2x ................(ii)
solving (i) and (ii), y = 50 m

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

Galileo Galilei (1564-1642) was an Italian Astronomer who

1) Discovered 4 satellites of Jupiter

2) Developed Telescope

3) Discovered that the movement of pendulum produces a regular time measurement

He is Physicist, Mathematician, inventor, and philosopher Too.