A abd B start walking towards Connaught Place from their respective positions, and move in straight roads with constant speeds. At the initial moment, A,B and Connaught place form a right triangle. After A travelled 30 km, the triangle became equilateral. When A arrived at connaught place, B still had to cover 6.66 km. to reach connaught place.
Find the initial distance between A and B.
(a)10 root 3
(b)12 root 3
(c)30 root 5
(d)20 root 3
(e) None of these
Plz give complete solution and time taken!
the ans is (d).
sol: let distance between A and B is y, and between B and CP is x. The triangle is right angled at B. Let A's speed is s1 and B's s2.
Now when A has traveled 30km , we have following relations;
30 = s1*t .......(1)
x-(sqrt(x^2+y^2)-30) = s2*t ........(2)
Also tan60 = y/x (since after A has traveled 30km, the triangle becomes an equilateral one, therefore angle ACB is 60)
we get: y=sqrt(3)*x
Put in (1) and (2) and divide them: u will get eqn; 2x^2-30x-200=0
solving it gives x=20