Correct Answer - Option 1 : 27/125
Given∶
A tennis ball is consistently bounces back 3/5 of the height from which it is dropped.
Formula Used∶
Geometric progression, Concept of Decreasing GP.
GP whose common ratio r lies between 0 and 1.
Calculation∶
Each time the ball is dropped and it bounce back, it reaches 3/5 of the height it was dropped from.
After the first bounce, the ball will reach 3/5 of the height from which it was dropped. Let it was the original height.
After the second bounce, the ball will reach 3/5 of the height it would have reached after the first bounce.
So, at the end of the second bounce, the ball would have reached 3/5 × 3/5 of the original height = 9/25th of the original height.
After the third and the last bounce, the ball will reach 3/5 of the height it would have reached after the 2nd bounce.
So, at the end of the last bounce, the ball would have reached 3/5 × 3/5 × 3/5 of the original height = 27/125 of the original height.
∴ The required fraction is 27/125 of its original height.