Quant Boosters  Swetabh Kumar  Set 3

Draw 3x+2y = 60 and 2x+3y = 60
find the common region as per question
a triangle will be formed with cordinates (12,12 ) ( 0,20 ) ( 0,30 )
area of this triangle = 60
use picks theorem : A = i + b/2  1
61 = i + b/2
calculate the number of boundary pts of triangle boundary , total 20 boundary pts will be there
9 on the vertical line between 0,20 and 0,30
3 on the line between 0,20 and 12,12
5 on the line between 0,30 and 12,12
3 vertices
total 20 boundary points
61  20/2 = 51 integral points

shouldn't it be 89.7 mins?
You might have missed 18 seconds both men have moved while from the moment the train meets the second man to the moment it passes him.
so reqd time = {600(T+v2)600(v1+v2)18(v1+v2)}/(v1+v2)
which gives 540018 seconds or 89.7 mins

We can do it another way too:
Put x= y,
F(2x) = f(x)^2
Put y=2x
F(3x)= f(x)^3
=>f(nx)=f(x)^nF(8)=F(2×4)=f(4)^2=1/9