<PRE><B>Question 627583</B>
Let the no. of students who have ridden airplane be A, the no. of students who have ridden boat be B and that who have ridden train be C.


Further, let the no. of students who have ridden only airplane be A&#39;, the no. of students who have ridden only boat be B&#39; and that who have ridden only train be C&#39;.

If the total number of students be N then we have

N = A&#39; + B&#39; + C&#39; + A&amp;#8745;B + B&amp;#8745;C + C&amp;#8745;A + A&amp;#8745;B&amp;#8745;C ________ (1)


Also, we know
A&#39; = A - A&amp;#8745;B - C&amp;#8745;A ________ (2)
B&#39; = B - A&amp;#8745;B - B&amp;#8745;C ________ (3)
C&#39; = C - B&amp;#8745;C - C&amp;#8745;A ________ (4)


Substituting in the equation (1) we have

N = A + B + C - A&amp;#8745;B - B&amp;#8745;C - C&amp;#8745;A + A&amp;#8745;B&amp;#8745;C __________ (5)

Now let us list all the values that we have:
N = 40, A = 17, B = 28, C = 10, A&amp;#8745;B = 12, C&#39; = 3, A&#39; = 4


Substituting all these values into equation (5)
40 = 17 + 28 + 10 - 12 - (B&amp;#8745;C + C&amp;#8745;A) + A&amp;#8745;B&amp;#8745;C
40 = 17 + 28 + 10 - 12 - (C - C&#39;) + A&amp;#8745;B&amp;#8745;C [Using equation (4)]
40 = 17 + 28 + 10 - 12 - (10 - 3) + A&amp;#8745;B&amp;#8745;C
A&amp;#8745;B&amp;#8745;C = 4


Answer: The no. of students who have ridden all modes of transportation is 4.</PRE>