Question

Two towers A and B of heights 200 ft and 150 ft respectively. The distance between the base of the towers is 250 ft. Two birds on top of each tower fly down with the same speed and meet at the same instant on the ground to pick up a grain. What is the distance between the foot of the tower A and the grain?

• A. 125 ft
• B. 90 ft
• C. 100 ft
• D. 150 ft

Answer 1

The correct option is B

90 ft

Height of Tower A =200 ft
Let x ft be distance between the grain and the base of tower A.
The distance flown by bird A is $OA=\sqrt{{200}^2+x^2}$ (By Pythagoras therorem)
Height of Tower B =150 ft
The distance from the base of Tower B to the grain is (250 -x).
The distance flown by bird B is $OB=\sqrt{{150}^2+(250-x{)}^2}$ (By Pythagoras therorem)
Since they arrived at the same time and traveled at the same speed, the two distances are equal.
$\sqrt{{200}^2+x^2}=\sqrt{{150}^2+(250-x{)}^2}$
Squaring both sides we get:
$40000+x^2=85000-500x+x^2,x=\frac{45000}{500}=90ft$