Question
The ratio of the speed of 'B' to that of 'C' is 1:2. 'B'
covers 'I' km in 9 hours and 'C' covers (I + 90) km in 6 hours. Find the time taken by 'D', whose speed is 50% of the combined speed of 'B' and 'C' together, to cover (I + 180) km.Solution
ATQ, Let the speed of 'B' and 'C' be f km/h and 2f km/h respectively. So, I = (f) × 9 = 9f -------------- (i) And (I + 90) = (2f) × 6 -------------- (ii) Using value of 'I' from equation (i) in equation (ii), we get 9f + 90 = 12f Or, 3f = 90 Or, 'f' = (90/3) = 30 So, speed of 'B' = 30 km/h Also, speed of 'C' = 2 × 30 = 60 km/h Therefore, speed of 'D' = 0.50 × (30 + 60) = 45 km/h And I = 9 × 30 = 270 km So, required time = {(270 + 180) / 45} = 10 hours
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