Rajiv can do a piece of work in 10 days, Venky in 12 days and Ravi in 15 days.…
2024
Rajiv can do a piece of work in 10 days, Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed?
- A.
5
- B.
6
- C.
9
- D.
7
Attempted by 637 students.
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Correct answer: D
Answer: 7
Step-by-step solution:
Work rates: Rajiv = 1/10 per day, Venky = 1/12 per day, Ravi = 1/15 per day.
If the job finishes in x days, Rajiv works 2 days → contribution = 2/10.
Venky leaves 3 days before finish, so he works x - 3 days → contribution = (x - 3)/12.
Ravi works the whole time x days → contribution = x/15.
Total work = 1, so set up the equation: 2/10 + (x - 3)/12 + x/15 = 1.
Clear denominators by multiplying both sides by 60: 12 + 5x - 15 + 4x = 60.
Simplify: 9x - 3 = 60 → 9x = 63 → x = 7.
Therefore, the work is completed in 7 days.