In an 800-meter race involving 'Amit', 'Bhanu', and 'Chinky', calculate the distance 'Amit' was ahead of 'Chinky'. Statement I : 'Amit' finishes 160 meters ahead of 'Bhanu'. Statement II: The speed of 'Bhanu' compared to 'Chinky' is in the ratio of 8:9.

ATQ, We know that when time is constant, ratio of distance covered = ratio of speed Statement I: Ratio of distance covered by 'Amit' and 'Bhanu' = 800:(800 - 160) = 800:640 = 5:4 So, data in statement I alone is not sufficient to answer the question. Statement II: Ratio of speeds of 'Bhanu' and 'Chinky' = 8:9 So, data in statement II alone is not sufficient to answer the question. On combining both statements, we have; Ratio of speeds of 'Amit' and 'Bhanu' = 5:4 And ratio of speeds of 'Bhanu' and 'Chinky' = 8:9 So, ratio of speeds of 'Amit', 'Bhanu' and 'Chinky' = 10:8:9 So, distance covered by 'Chinky' in the time taken by 'Amit' to cover 800 metres = 800 × (9/10) = 720 metres So, 'Amit' beat 'Chinky' by 800 - 720 = 80 metres So, the data in both statements I and II together is necessary to answer the question.