UPSC Prelims 2021 · CSAT
Question 16: Basic Numeracy
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 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 ?
AnswerUPSC’s answer is (b).
Each bounce reaches four-fifths of the previous height. Starting from a 150 cm drop, the rebounds are 120, 96, 76.8, 61.44 and 49.15 cm, one after each touch of the ground. The first four rebounds are all above 50 cm. The fifth rebound, to 49.15 cm, is under 50 cm, so UPSC treats it as the last bounce: the ball has touched the ground five times. Remember: write out the sequence term by term, stop at the first height under the limit, and count ground contacts, not heights.
Why each option is right or wrong
- (a) 4 contacts leave the ball rebounding to 61.44 cm, still above 50 cm.
- (b) Right: after the fifth contact the rebound is 49.15 cm, under 50 cm, so bouncing ends.
- (c) 6 counts the ball's fall from 49.15 cm; UPSC treats the fifth rebound as the last bounce.
- (d) 7 goes well past the point where the height falls below 50 cm.
Worth knowing: The ball falls again from 49.15 cm and touches the ground a sixth time, so 6 is arguable; UPSC's key counts only up to the rebound that falls under 50 cm.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.