Question
A and B alone can complete a work in 20 and 80 days,
respectively. 50% of the work is completed by C in 5x days, and the remaining work is completed by A and B working together in ‘x’ days. Find the time taken by B and C to complete the whole work while working together.Solution
Time taken by A and B to complete the whole work while working together = (20 × 80)/(20 + 80) = 16 days So, x = 16/2 = 8 (Since, 50% of the work is done by A and B together) As, time taken by C to complete 50% of the work = 8 × 5 = 40 days So, time taken by C to complete the entire work = 40 × 2 = 80 days Therefore, time taken by B and C to complete the whole work while working together = (80 × 80)/(80 + 80) = 40 days
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