A can beat B in a 100-metre race by 10 metres. B can beat C in a 100-metre race by 10 metres. What is the ratio (t_A : t_B : t_C), which are the respective times taken by A, B and C to complete the race?

81 : 90: 100

Given, 

B + 10 = A, C + 10 = B,

Therefore , A : B = 100 : 90

and B : C = 100 : 90,

⇒ A : B : C = 100 : 90 : 81

⇒ (t_A : t_B : t_C) = \(\frac{1}{100}\) : \(\frac{1}{90}\) : \(\frac{1}{81}\)

⇒ LCM = 8100

⇒ Required ratio = 81 : 90 : 100.