Question
The day efficiency of Rajeev is equal to the one-day
efficiency of Divya and Vivek together. Divya is 25% more efficient than Vivek and starts with 20% more of his efficiency with Vivek and works for x days, after that Divya left the work and remaining work will be completed by Vivek and Sanjay together in (x + 10) days. If ratio of work done by Divya and Vivek together to work done by Vivek and Sanjay is 5:7 and efficiency of Sanjay is 50% less than Vivek. Then Rajeev and Sanjay complete work together in how many days?Solution
Ratio of efficiency of Divya: Vivek = 125:100 = 5: 4 Efficiency of Sanjay = 4 × (1/2) = 2 units/day According to question, (5 × (120/100) + 4) x / (4 + 2) (x + 10) = 5/7 10x / (6x + 60) = 5/7 70x – 30x = 300 x = 7.5days Total work = (10 × 7.5) + (6 × 17.5) = 75+105 = 180 ATQ-Rajeev efficiency = (Divya + Vivek) = 9 units/day Sanjay and Rajeev efficiency = (2 + 9) = 11 units/day (Sanjay + Rajeev) = 180/11 days
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