Question : Directions: It took 20 days for all the leaves of a tree to fall. If the number of leaves that fell each day was twice that of the previous day, on which day would the tree be half bare?
Option 1: 10th day
Option 2: 11th day
Option 3: 40th day
Option 4: 19th day
Correct Answer: 19th day
Solution : Let the total number of leaves on the tree be A.
The number of leaves that fell each day = 2 × (the number of leaves that fell on the previous day)
On the 20th day, all leaves fell.
The number of leaves fell on 20th day = 2 × (the number of leaves fell on the 19th day)
⇒ A = 2 × (the number of leaves fell on the 19th day)
⇒ The number of leaves fell on the 19th day = $\frac{A}{2}$ = half of the total leaves.
So, on the 19th day, the tree will be half bare. Hence, the fourth option is correct.
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