Question

Out of two trees, some distance apart the height of the bigger one is 5 times that of the
smaller one. Sometime after sunrise the shadows of the tops of the two trees fall at the same
place. In this case the length of the shadow of the bigger tree is 8 metres more than thrice the
length of the shadow of the smaller tree. Find (a) the length of the shadow of the smaller tree;
(b) the distance between the two trees.

Answer 1

Out of two trees, some distance apart the height...

• Assume x=length of the smaller tree and 5x=the lengthof the bigger tree.
• y=length of shadow of smaller tree and 3y+8=length of shadow of big tree.
• X/5X=y/3y+8 (cut both the xs)
• 3y+8=5y
• 8=2y
• y=4
• Length of shadow is 4 metres
• Distance=3y+8-y=2y+8=2(4)+8=16 metres

Answer 2

(a) the length of the shadow of the smaller tree = 4 m

(b) the distance between the two trees = 16 m

• From given data, let us assume  
• length of the smaller tree = x  
• the length of the bigger tree = 5x    
• (∵ the height of the bigger one is 5 times that of the smaller one)
• length of the shadow of a smaller tree = y  
• length of the shadow of a big tree = 3y+8    
• (∵ the length of the shadow of the bigger tree is 8 metres more than thrice the length of the shadow of the smaller tree)
• (a) the length of the shadow of the smaller tree
• Now,
• $\dfrac{x}{5x} = \dfrac{y}{3y+8}\\\\\dfrac{1}{5} = \dfrac{y}{3y+8}\\\\3y+8 = 5y\\\\8 = 2y\\\\y = 4$
• Length of the shadow of smaller tree  y = 4 m
• (b) the distance between the two trees.
• Distance = 3y+8-y = 2y+8 = 2(4)+8 = 16 m