QUESTION

CSAT

Easy

Maths

Prelims 2021

A boy plays with a ball, and he drops it from a height of $1.5$ m. Every time the ball hits the ground, it bounces back to attain a height $\frac{4}{5}$ th of the previous height. The ball does not bounce further if the previous height is less than $50$ cm. What is the number of times the ball hits the ground before the ball stops bouncing?

Select an option to attempt

Explanation

Given Height = $1.5$ m = $1.5 \times 100$ cm = $150$ cm

When ball hits the ground for the 1st time, its height = $(\frac{4}{5}) \times 150 = 120$ cm

When ball hits the ground for the 2nd time, its height = $(\frac{4}{5}) \times 120 = 96$ cm

When ball hits the ground for the 3rd time, its height = $(\frac{4}{5}) \times 96 = 76.8$ cm

When ball hist the ground for the 4th time, its height = $(\frac{4}{5}) \times 76.8 = 61.44$ cm

When ball hits the ground for the 5th time, its height = $(\frac{4}{5}) \times 61.44 = 49.15$ cm

Since, it is given that if the previous height is less than $50$ cm, the ball does not bounce further. So we can say that after the ball hits the ground for the 6th time, it doesn't bounce back.

Hence, option (c) is the correct answer.

Trusted by 2L aspirants